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RADIOACTIVITY AND NUCLEAR ENERGY

P.1

1

HKCEE – PAPER I

2011 – 7

It is known that plutonium-238 (238

94 Pu) decays by emitting one particle.

(a) Write a nuclear equation for the decay of plutonium-238. Use the symbol Y as the daughter

nucleus. (2 marks)

(b) A sample of plutonium-238 is put in a cloud chamber. Some tracks are seen.

(i) Describe the tracks that are seen. (1 mark)

(ii) No tracks can be seen when the sample is covered by a piece of paper. Explain.

(2 marks)

(c) Plutonium-238 can be used in heater units in spacecrafts for outer space missions. It is

known that the power of the heater unit is directly proportional to the activity of

plutonium-238 contained. Each heater unit has a power of 2 W when it is newly

manufactured. How long can a newly manufactured heater unit last if the minimum

power output required is 0.25 W ?

Given : half-life of plutonium-238 = 87.7 years (3 marks)

2009 – 7

Radon-222 (Rn-222) has a half-life of 3.8 days and undergoes a radioactive decay series as shown in

Figure 8 to become a stable nuclide Lead-206 (Pb-206).

Figure 8

(a) Estimate the mass of undecayed Rn-222 after 15.2 days if its initial mass is 1 10-5

g.

(2 marks)

(b) State the nuclear radiation emitted in the process (1) indicated in Figure 8. (1 mark)

(c) Write down the nuclear equation for process (2) indicated in Figure 8. (2 marks)

(d) Determine the total number of particles and the total number of particles emitted in the

radioactive decay series from Rn-222 to Pb-206. (4 marks)

2008 – 12

(a) A teacher places a radioactive source 1 cm in front of a Geiger-Muller tube (GM tube) and

measures the count rate. When he inserts a piece of paper between the radioactive source and

the GM tube, he finds that there is no significant change in the measured count rate. State the

conclusion about the type of radiation emitted from the radioactive source. (1 mark)

The teacher then conducts another experiment to investigate the deflection of radiations inside

a magnetic field as shown in Figure 2.3. the GM tube can be rotated from 0o to 180

o around

the magnetic field. Figure 24 shows the count rate recorded at different angles with or

without the magnetic field.

Atomic number 82 83 84 85 86

Mass number

206

214

216

222

218

220

Rn

Po

(1)

Pb

Pb

Po

Bi (2)


P.2

2

Figure 23

Figure 24

(b) Estimate the count rate due to the background radiation. (1 mark)

*(c) Using the result in Figure 24, explain why it can be concluded that the radioactive source

emits and rays. (5 marks)

(d) Estimate the count rate due to each type of radiation at = 90o without the magnetic field.

Write the answer in Table 3. (2 marks)

Table 3

Type of radiation Count rate / counts per minute

0

0o

GM tube connected

to counter

region with magnetic field

pointing into paper

90o

180o

radioactive source

in a lead box

Recoded count rate / counts per minute

250

200

150

100

50

0 50 90 180

/ o

with magnetic field

without magnetic field


P.3

3

2007 – 8

In a physics lesson, a teacher uses the apparatus shown in Figure 13 to find the range of particles in

the air. Describe the procedures of the experiment. (5 marks)

Figure 13

2006-8

Workers of nuclear plants are required to wear film badges (see Figure 14) to monitor their exposure to

radiation. Inside the film badge, an opaque plastic bag is wrapped around a sheet of photographic film.

Aluminium and lead sheets are also placed inside the badge (see Figure 15) so that the types of

incoming radiation can be distinguished.

(a) What type(s) of radiation can be detected by the badge? (1 mark)

(b) Why is an opaque plastic bag used to wrap the photographic film? (1 mark)

(c) The film of three workers John, Mary and Ken were developed. Table 3 shows the degrees of

blackening on different regions of the films inside the badges which they wore.

Regions on the film Degree of blackening (0 – 5)

(0 = not blackened; 5 = most blackened)

John Mary Ken

Beneath the open window 5 5 5

Beneath the 1 mm aluminium sheet 5 3 4

Beneath the 3 mm aluminium sheet 5 1 2

Beneath the 5 mm lead sheet 4 0 0

Table 3

*(i) Based on the results in Table 3, explain which type(s) of radiation John and Mary are

definitely being exposed to respectively. (4 marks)

(ii) Give on reason why different degrees of blackening were recorded on the films of Mary

and Ken. (1 mark)

(d) Suggest one hazard of exposure to ionizing radiations. (1 mark)


P.4

4

2005 – 7

Read the following passage about Iodine-131 therapy and answer the questions that follow.

Iodine-131 is a radioisotope which emits and radiations. It can be used for thyroid cancer

treatment.

A patient suffering from thyroid cancer will first undergo an operation to have the thyroid gland

removed. However, some thyroid tissue may remain in the neck of the patient or may be carried in the

blood stream to other parts of the body. Iodine-131 is then used to trace and get rid of the remaining

thyroid tissue in the body.

Iodine-131 therapy consists of two stages. In Stage 1, the patient will take a low does of Iodine-131 to

trace the remaining thyroid tissue. A detector is placed near the patient to monitor the activity of the

radiation coming from the patient.

In case any remaining thyroid tissue is spotted in State 1, the patient will then take a higher dose of

Iodine-131 in Stage 2. The iodine will be absorbed by the thyroid tissue and the radiation emitted can

kill the cancer cells.

Special hospital rooms are designed for patients who receive Stage 2 of the therapy. The rooms have

metallic shielding in the doors and reinforced walls. Inside the rooms, there are plastic covers on the

furniture, doors, handles and switches.

Source: Iodine-131 Therapy, The Ohio State University Medical Center, 2003.

(a) Explain why, in Stage 1, radiation from the patient cannot be detected by the detector.

(1 mark)

(b) In Stage 2, which kind of radiation is more effective in killing caner cells? Explain you

answer. (2 marks)

(c) State one special feature of the hospital rooms designed for patients receiving State 2 of the

therapy and explain its function. (2 marks)

2005 – 8

Carol performs an experiment to measure the half-life of a radioactive source. She places a Geiger-

Muller tube in front of the source and the following results are obtained:

Time t / hour 0 10 20 30 40 50 60 70

Count rate / counts per

minute

400 225 154 119 107 105 100 102

Table 1

(a) Plot a graph of the count rate against time in Figure11. (4 marks)

(b) Estimate the background count rate. (1 mark)

(c) Estimate the corrected count rate at t = 0.

Hence, or otherwise, estimate the half-life of the source. (2 marks)

2004 – 9

Figure 15

Figure 14

slot

electrode

americium source

to an alarm circuit


P.5

5

Figure 14 shows a smoke detector. The circuit inside the detector is shown in Figure 15. A small

amount of the radioisotope americium-241 ( Am24195 ) is placed between two electrodes. The two

electrodes are connected to a battery and an alarm circuit. The detector has slots in it to allow air flow.

(a) An americium-241 nucleus decays by emitting an -particle to form a daughter nucleus

neptunium (Np), with a half-life of 432 years.

(i) Write down an equation for the decay of an americium-241 nucleus. (2 marks)

(ii) Find the number of neutrons in the daughter nucleus. (1 mark)

(b) Under normal conditions, a small current flows in the circuit inside the detector. However,

when smoke particles enter the detector, the current drops significantly. This triggers the

alarm to sound.

*(i) Explain why a current flows between the electrodes under normal conditions.

(4 marks)

(ii) Suggest one possible reason why the current drops when smoke particles enter the

detector. (2 marks)

(c) Explain why it is preferable for the radioactive source used in smoke detectors to have a long

half-life. (2 marks)

(d) Carbon-14 ( C146 ) is a radioisotope which decays by emitting particles and has a half-life of

5700 years. Explain whether this source is suitable for use in smoke detectors or not.

(2 marks)

(e) People are concerned about the biological hazards of radiation. If you are the manufacturer of

the described smoke detector, how would you explain to the public that using the detector will

not pose any health hazard? (2 marks)

2003 – 9

In April 1986, a disastrous nuclear accident happened at the Chernobyl Nuclear Station. A large

amount of radioactive substances was released and spread to neighbouring counties. The radiation

levels recorded in these countries were much higher than the normal background count rate.

(a) State two sources of background radiation. (2 marks)

(b) State one way by which the radioactive substances released in the accident were spread to

neighbouring countries. (1 mark)

(c) One of the radioactive isotopes released in the accident was caesium-137 (Cs-137). The

following equation shows how Cs-137 is produced:

nRbCsnU 1037

13710

23592 z

yx

(i) If z = 4, find the values of x and y and state their physical meanings. (4 marks)

(ii) The half-life of Cs-137 is 30 years. Suppose that a soil sample contaminated by Cs-

137 was found to have an initial activity of 1.2 106 Bq (disintegrations per second).

A physicist comments that the contaminated sample will affect the environment for

more than 300 years. Justify the physicist’s claim with calculations. You may

assume that the activity of a non-contaminated sample of similar nature is 200 Bq.

(3 marks)

*(d) The development of nuclear energy is a controversial issue. Do you support the development

of nuclear energy? State your reasoning to support your point of view. (5 marks)

2002 – 10

Figure 15

Iodine ( I13153 ) is a radioisotope which decays by emitting a -particle and rays. It is used in hospitals

to test the kidneys of patients. During the test, an iodine-131 solution is injected into the bloodstream

of a patient. As the blood passes through the kidney, iodine-131 will be absorbed by the kidney and

eventually excreted out of the body with urine. If the kidney is not functioning properly, both the

absorption and excretion rates of iodine-131 will decrease. A -detector is placed near the kidneys of

the patient to detect the activity of the radiation coming from the kidneys (see Figure 15).

-detector


P.6

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(a) Using X to denote the daughter nucleus, write down an equation for the decay of iodine-131

nucleus. (2 marks)

(b) Explain why the -particles emitted by iodine-131 fail to reach the detector. (1 mark)

(c) The half-life of iodine-131 is 8 days.

(i) State the meaning of 1half-life’

(ii) For safety purposes, the activity of iodine-131 solution in the test should not exceed

1.5 108 disintegrations per second. When an iodine-131 solution is prepared, its

activity is 6 108 disintegrations per second. How many days after preparation

would the solution be suitable for the test? (2 marks)

(iii) Figure 16 shows the variation of the activities of the radiation detected from the right

and left kidneys of a patient with time.

Figure 16

Which kidney do you think is not functioning properly? Explain your answer.

(3 marks)

*(iv) Besides iodine-131, technetium-99m is another radioisotope which is used in the

kidney test. Technetium-99m emits radiation only and its half-life is 6 hours.

Which of these two sources do you think is more preferable for use in the kidney

test? Explain you answer. (5 marks)

2001 – 11

Figure 14

Figure 14 shows a set-up used to study the radiation from a radioactive source. A Geiger-Muller (GM)

tube is placed at position P, which is 20 cm from the source. Two coils A and B connected to a battery

and a switch S are placed between the source and the GM tube as shown. Initially, S is open and the

variation of the count rate recorded by the GM tube with time is shown in Figure 15.

Figure 15

(a) Explain why the count rate shown in Figure 15 is not due to particles, no matter what kind

of radiation are emitted by the source. (2 marks)

(b) Now switch S is closed. The GM tube is placed at positions P and Q in turn (see Figure 14)

and the count rates recorded are shown in Figure 16 and 17 respectively. When the GM tube

is placed at any point vertically above P, an average count rate of 100 counts per minute is

recorded at each point.

Activity/disintegrations

per second

Time/min

Left kidney

Right kidney

0

S

Q

P Radioactive

source

Vertical line Lead

block

20 cm

Battery

GM tube

A

B

Time 0

1000

Recorded count rate at P/

counts per min


P.7

7

Figure 16 Figure 17

(i) State the direction of the magnetic field formed between coils A and B. (1 mark)

(ii) What kind of radiation is recorded when the GM tube is held at any point vertically

above P? Explain your answer. (3 marks)

*(iii) What conclusion about the radiation emitted by the source can you draw from

Figures 16 and 17? Explain your answer. (5 marks)

(iv) Explain why the sum of the average count rates recorded in Figures 16 and 17 is

greater than that recorded in Figure 15. (2 marks)

(c) The above experiment cannot determined whether particles are emitted by the

source. Suggest a method for finding out the answer. (2 marks)

2000 – 11

(a) X and Y are two radioactive nuclides with half lives of 12 hours and 2.6 years respectively.

Both nuclides decay by emitting particle to form stable product nuclides.

(i) After emitting particle, how would the atomic number and mass number of nuclide

X be changed (2 marks)

(ii) Describe the changes in activity (in disintegrations per second) of a specimen of

nuclide X and a specimen of Y after one day. (2 marks)

(iii) Comment on the following statement:

The mass of a specimen of a nuclide X will be reduced by approximately half in 12

hours. (2 marks)

(b) A factory produces aluminium sheets 1 mm in thickness. The thickness of the sheets is

monitored by a gauge. (See Figure 16.) A source is used in the gauge.

*

Figure 16

(i) Explain why and sources are not used in the gauge. (2 marks)

(ii) Which of the nuclides (X or Y) is more suitable to use as the radioactive source?

Explain your answer. (2 marks)

*(iii) The count rate recorded should be around 90 counts per second when the thickness of

the aluminium sheet is 1 mm. In a certain day when the gauge is operating properly,

the following data are recorded:

Time/s 0 10 20 30 40 50 60 70 80 90 100

Recorded count

rate/counts per s

90 89 91 90 90 88 66 64 90 89 89

Table 3

Describe and explain the variation in the readings in Table 3. (5 marks)

HKCEE – PAPER II

2011 – 22

Which of the following statements about , and radiations is incorrect ?

A. Only radiation can travel through a vacuum.

B. radiation can be stopped by an aluminium plate of 5 mm thick.

C. particles are fast moving electrons.

D. radiation can blacken a photographic film.

Time 0

400


counts per min

Time 0

650


counts per min

Aluminium sheet

Detector

Radioactive

source

To counter


P.8

8

P

Q

R

X

Y

radioactive source

in a lead box

+5000 V

0 V

GM tube

2011 – 23 A radioactive source is put in front of a GM tube. The initial count rate is 1050 counts per minute. It is

known that the half-life of the source is 4 hours and the background count rate is 50 counts per minute.

What is the most likely count rate (in counts per minute) after 8 hours ?

A. 50

B. 125

C. 250

D. 300

2011 – 24

A 23892 U nuclide undergoes a certain number of and decays and becomes 210

82 Pb. Find the number

of particles emitted.

A. 2

B. 3

C. 4

D. 5

2011 – 27 1

st statement: In the production of X-ray, the speed of the X-ray depends on the speed of the

electron striking the heavy metal target.

2nd

statement: X-rays are produced when a heavy metal target is struck by fast moving electrons.

1st statement 2

nd statement

A. True True, and is a correct explanation of the 1st statement.

B. True True, and is not a correct explanation of the 1st statement.

C. True False

D. False True

2011 – 45

The figure above shows a radioactive source placed near two parallel metal plates X and Y that are

connected to a power supply. When a GM tube is moved along the dotted line ( ), the count rate

shows a significant increase at P and Q respectively. Which of the following statements is correct

when a magnetic field pointing out of the paper is applied between X and Y ?

A. The count rate at P decreases and the count rate at Q remains the same.

B. The count rates at P and Q remain the same.

C. The count rate at P decreases and the count rates at Q and R increase.

D. The count rates at P, Q and R are equal.

2009 – 24

n e H H H 42

31

21

Which of the following descriptions about the nuclear reaction above is correct?

A. It is nuclear fission.

B. It is nuclear fusion.

C. It is a chain reaction.

D. It is a radioactive decay.


P.9

9

2009 – 25

ZYXβα

The above shows part of a decay series. Which of the following deductions is/are correct?

(1) X and Z are isotopes of the same element.

(2) X has two more neutrons than Z.

(3) Z has one more proton than Y.

A. (1) only

B. (3) only

C. (1) and (2) only

D. (2) and (3) only

2009 – 26

The half-life of a radioactive sample is 15 hours. The initial count rate recorded is 1000 counts per

minute. After 15 hours, the count rate recorded becomes 528 counts per minute. What is the

background count rate? (Measured in counts per minute.)

A. 25

B. 28

C. 50

D. 56

2009 – 27

Which of the following conditions is/are necessary to sustain the chain reaction in the nuclear fission of

uranium-235?

(1) Each fission produces a large amount of energy.

(2) At least one neutron is released in each fission.

(3) Each fission produces two smaller nuclei.

A. (1) only

B. (2) only

C. (1) and (3) only

D. (2) and (3) only

2009 – 45

1st statement: particles are emitted from the radioactive nucleus in a decay.

2nd

statement: particles are fast moving electrons.

1st statement 2

nd statement

A. True True, and is a correct explanation of the 1st statement.


C. True False

D. False True

2008 – 24

Which of the following descriptions about the half-life of a radioactive substance is correct?

A. It is equal to half of the time for all the radioactive nuclei of the substance to decay.

B. It is equal to half of the time for a radioactive nucleus of the substance to decay.

C. It is equal to the time for the substance to reduce its mass by half.

D. It is equal to the time for half of the radioactive nuclei of the substance to decay.

2008 – 25

Which of the following actions will maximize a person’s exposure to radiation?

A. Using a GM tube and counter to measure the background radiation in laboratory.

B. Eating food that has been sterilized by exposure to gamma radiation.

C. Listening to radio.

D. Going for a flight to a distant place in a high-flying aeroplane.

2008 – 26

Which of the following nuclear reactions is a fission?

A. n3KrBanU 10

8936

14456

10

23592

B. e2PunU 01 -

23994

10

23592


P.10

10

C. n4EsNU 01

24899

147

23592

D. nHeHH 10

42

31

21

2008 – 27

Which of the following statements about particles is correct?

A. particles carry positive charge.

B. particles can be deflected by a magnetic field.

C. particles cannot be deflected by an electric field.

D. particles can be stopped by a sheet of paper.

2007 – 24

Susan performs an experiment in which a radioactive source is placed closely in front of a GM counter.

The graph below shows the variation of count rate with time.

Which is the half-life of the radioactive substance?

A. 4 minutes

B. 5 minutes

C. 8 minutes

D. 10 minutes

2007 – 25

In the upper atmosphere, neutrons are produced by the action of cosmic rays. These neutrons interact

with nitrogen nuclei as shown in the following reaction:

HNn 11

147

10 X

Element X will then emit a particle. The reaction is as follows:

01-YX

What is the final product Y?

A. C146

B. C136

C. C147

D. C137

2007 – 26

Some dangers substances are stored in a metal container inside a wooden box as shown in the figure

below. What metal should be used for the container and what type of substance is stored?

Metal used Type of substance stored

A. Iron Radioactive

B. Iron Flammable

C. Lead Radioactive

D. Lead Flammable

Count rate / counts per minute

Time / minute 0 4 8 12 16 20

100

200

300

400


P.11

11

2006 – 27

Some fresh foods are exposed to radiations from radioactive isotopes for a short time so that the

micro-organisms in the foods can be killed. Why are the irradiated foods not harmful to people who

eat them?

A. radiation is an electromagnetic wave.

B. radiation has a high penetrating power.

C. radiation does not have a high ionizing power.

D. radiation does not make the foods radioactive.

2006 – 42

A radioisotope X has a half-life of 2 days while another radioisotope Y has a half-life of 1 day. Initially

there are N undecayed atoms of X and 8 N undecayed atoms of Y. After how many days will X and Y

have the same number of undecayed atoms?

A. 3 days

B. 4 days

C. 6 days

D. 8 days

2006 – 43

SRQP

ZYX

In the above two decay series, P and Y are two isotopes. Which of the following pairs of nuclides are

isotopes to each other?

(1) X and R

(2) Y and S

(3) Z and Q

A. (1) and (2) only

B. (1) and (3) only

C. (2) and (3) only

D. (1), (2) and (3)

2005 – 24

A radioactive source is placed in front of a uniform magnetic field pointing into paper as shown above.

If a high count rate is recorded at positions P and Q, what kinds of radiation have been detected?

P Q

A.

B.

C.

D.

2005 – 25

A thorium nucleus ( Th23490 ) decays by emitting a particle to form a daughter nucleus X. Which of the

following equations represents this decay?

A. XTh 23088

23490

B. XTh 23489

23490

C. XTh 23390

23490

D. XTh 23491

23490

P

Q

source

lead castle

Geiger-Muller tube


P.12

12

2005 – 26

Which of the following nuclear reactions is a nuclear fusion?

A. n2KrBaU 9036

14456

23592

B. HCnN 11

146

147

C. nHeHH 42

31

21

D. Th23490

23892U

2004 – 40

neutron aZHH 41

21 y

x

Find the values of x and y in the above nuclear reaction.

x y

A. 2 1

B. 2 2

C. 3 1

D. 3 2

2004 – 41

Different absorbers are placed in turn between a radioactive source and a Geiger-Muller tube. Three

readings are taken for each absorber. The following data are obtained:

Absorber Count rate / s-1

- 200 205 198

Paper 197 202 206

5 mm aluminium 112 108 111

25 mm lead 60 62 58

50 mm lead 34 36 34

What type(s) of radiation does the source emit?

A. only

B. only

C. and only

D. , and

2004 – 42

In order to detect cracks in an underground oil pipe, an engineer proposes adding a radioactive source

to the oil. Which of the following sources is most suitable?

A. a soruce with a half-life of a few hours

B. a source with a half-life of several years

C. a source with a half-life of a few hours

D. a source with a half-life of several years

2003 – 40

Which of the following statements about particles and rays is/are correct?

(1) They can both be deflected by a magnetic field.

(2) particles have a stronger ionizing power than rays.

(3) They are emitted with almost the same speed in radioactive decay.

A. (1) only

B. (2) only

C. (1) and (3) only

D. (2) and (3) only

2003 – 41

Activity of P/Bq

800

400

0 10 Time /min

Activity of Q/Bq

800

200

0 10 Time /min


P.13

13

The figures above show the variation of the activities of two radioactive sources P and Q with time.

Find the ratio of the half-life of P to that of Q.

A. 1 : 1

B. 1 : 2

C. 2 : 1

D. 4 : 1

2003 – 42

Which of the following are essential criteria in choosing radioactive sources as medical tracers in

human bodies?

(1) The sources should have a short half-life.

(2) The radiation emitted should have a weak ionizing power.

(3) The radiation emitted should not be deflected by an electric field.

A. (1) and (2) only

B. (1) and (3) only

C. (2) and (3) only

D. (1), (2) and (3)

2002 – 40

A radioactive isotope Th23490 undergoes a series of decay processes to form a daughter nuclide Th206

82 .

How many -particles and -particles have been emitted in this decay process?

No. of -particles No. of -particles

A. 6 7

B. 7 6

C. 7 8

D. 8 7

2002 – 41

Which of the following particles cannot be deflected by a magnetic field?

A. -particles

B. -particles

C. neutrons

D. protons

2002 – 42

Which of the following is/are application(s) of radioactiviy?

(1) estimate the age of ancient remains

(2) to kill bacteria in food

(3) to transmit signals over long distances

A. (2) only

B. (3) only

C. (1) and (2) only

D. (1) and (3) only

2001 – 39

Radium ( Ra22688 ) decays by emitting an particle to form a product nucleus X. Which of the following

shows the correct equation for this decay?

A. XRa 22286

22688

B. XRa 23090

22688

C. XRa 22484

22688

D. XRa 22286

22688

E. XRa 22289

22688

2001 – 40

The initial activity of a radioactive isotope is 2000 disintegrations per second. After 4 hours, the

activity of the isotope drops to 125 disintegrations per second. Find the half-life of the isotope.

A. 15 minutes


P.14

14

B. 30 minutes

C. 48 minutes

D. 60 minutes

E. 80 minutes

2001 – 41

SRQP

The above shows part of a radioactive series. Which of the following nuclei are isotopes of the same

element?

A. P and Q

B. P and S

C. P and R

D. Q and S

E. Q, R and S

2000 – 40

Which of the following statements about particles and rays is correct?

A. Both of them carry charges.

B. Both of them are transverse waves.

C. Both of then can be deflected by a magnetic field.

D. Both of them have strong ionizing power.

E. Both of them can travel through a vacuum.

2000 – 41

Which of the following is not a safety precaution for handling radioactive sources?

A. Radioactive sources should be handled with forceps.

B. Users should not eat or drink when handling radioactive sources.

C. Users should wash their hands after handling radioactive sources.

D. Radioactive sources should not be held close to the eye for visual examination.

E. Radioactive sources should be stored in wooden boxes after use.

2000 – 45

1st statement: sources are not suitable for injection into human bodies as medical tracers.

2nd

statement: particles carry positive charges and can be deflected by electric fields.

1st statement 2

nd statement

A. Ture True, and is a correct explanation of the 1st statement.


C. True False

D. False True

E. False False

HKAL – PAPER I

2010 – 4

(a) A nucleus of radon (222

86 Rn) decays to an isotope of polonium (Po) by emitting an -particle.

Given: mass of a radon nucleus = 222.0176 u

mass of a polonium nucleus = 218.0090 u

mass of an -particle = 4.0026 u

1 u = 1.66 1027

kg, which is equivalent to 931 MeV

charge of an electron e = 1.60 1019

C

(i) Write an equation for the decay and find the energy released, in MeV, in the decay.

(3 marks)

(ii) The energy released in the decay becomes the kinetic energy of the decay products.

Explain quantitatively why the -particle takes most of the energy and find its speed v.

Assume that the parent nucleus is at rest initially. (4 marks)

(b) (i) -particles with the speed v found in (a)(ii) are directed into an evacuated region with a

uniform magnetic field B = 0.5 T normal to the initial velocity of the -particles as shown

in Figure 4.1. Find the radius of the path described by the -particles in the field region.


P.15

15

Given: the charge to mass ratio of an -particle is 4.82 107 C kg

1 (2 marks)

Figure 4.1

(ii) Explain whether the -particles would emerge with a greater speed from the field.

(2 marks)

2009 – 8

Carbon-14 dating is used to determine the age of archeological sample by measuring its activity due to

the carbon-14 remaining in it.

(Given: molar mass of carbon-12 = 12.0 g, half-life of carbon-14 t1/2 = 5730 years and 1 year is

equivalent to 3.15 107 seconds)

(a) (i) Calculate the decay constant , in s-1

, of carbon-14. (2 marks)

(ii) It is known that the relative abundance of carbon-14 in living things is that there is

only one carbon-14 atom for every 7.2 1011

atoms of carbon-12. Determine the

number of carbon-14 atoms decaying per second for 1 g of carbon in living things.

(3 marks)

(b) (i) Explain the origin of carbon-14 in the atmosphere and why the abundance of carbon-

14 in living things, such as plants, remains more or less constant. (3 marks)

(ii) After corrected for background radiation, an archeology measured an activity of 20

disintegrations per minute from 10 g of carbon in a piece of bone. Use the result in

(a) to determine the approximate age of the bone. (3 marks)

(c) Give one reason why carbon-14 dating needs correction as there have been open-air nuclear

tests since 1940. Explain how the result of dating would be affected without such corrections.

(3 marks)

2003 – 8

(a) The graph shows the number of ion-pairs produced per mm by a certain type of nuclear

radiation versus distance along its track in air.

(i) What type of nuclear radiation is represented by the graph? Given one piece of

evidence. (2 marks)

(ii) Use the graph to estimate

(I) the total number of ion-pairs produced by the radiation. (2 marks)

(II) the total energy of the radiation in MeV. (3 marks)

(Given: average energy required to produce an ion-pair is 5 10-18

J

electronic charge, e = 1.6 10-19

C)

(iii) Explain why there is a peak near the end of the track. (1 mark)

(b) ZYXγβγβ

,,

The above series shows the decay of a radioactive isotope X to isotope Y and finally to isotope

Z. The half-lives of X and Y are 24 days and 72 s respectively. The half-life of Z is much

× × × × × ×

× × × × × ×

× × × × × ×

× × × × × ×

× × × × × ×

× × × × × ×

-particles

of speed v

uniform magnetic

field B pointing

into the paper

0 10 20 30 40 50 60 70 80

Distance traveled

from source / mm

No. of ion-pairs

formed per mm

8000

6000

4000

2000


P.16

16

longer than 24 days. The disintegration of both X and Y would each emit a - and - radiation.

A sample containing 1 mg of pure X only is prepared initially.

(Given: Avogadro constant = 6.02 1023

mol-1

Molar mass of X – 234.0 g)

(i) Find the total number of nuclear radiations that could be emitted from the sample.

(2 marks)

(ii) Estimate the time required for the activity of the sample to decrease by 10 %.

(3 marks)

1999 – 5

People are often killed in a fire as a result of suffocation. To

minimize the loss of lives, smoke detectors can be installed in

buildings and a loud sound and a flashing light are triggered when

smoke is detected. Figure 5.1 shows a common ionization smoke

detector which has a small radioactive source inside. During normal

operation, the radioactive source keeps emitting ionizing particles

and a certain ionization current is maintained inside the chamber of

the detector.

Figure 5.1

(a) The manufacturer claims that the radioactive source in the smoke detector presents no hazard

to health in normal use. Comment on this claim and briefly explain which type of radioactive

source should be used in the smoke detector. (3 marks)

(b) When the radioactive source in the detector is placed close to a GM-tube, the count rate

measure is 2000 s-1

. The average number of ion-pairs produced by each radiation particle is 4105 and each ion carries a charge of 19106.1 C.

(i) Estimate the maximum ionization current in the smoke detector. Why is the

ionization current in the smoke detector significantly less than this maximum value?

(3 marks)

(ii) The smoke detector should be disposed of when its maximum ionization current

drops below 12105 A. The manufacturer claims that the life of the detector is 10

years. Estimate the half-life of the radioactive source used in the detector. (3 marks)

1998 – 5

A reaction which takes place in the core of a nuclear reactor is described by the following equation:

MeV 174.4n3KrBanU 10

9136

14656

10

23592

Mass of one nuclide of U23592 =235.0439 u

Mass of one nuclide of Ba14256 =141.9164 u

Mass of one nuclide of Kr9136 =90.9234 u

1 u (atomic mass unit) 2710660.1 kg, which corresponds to 934 MeV

(electronic charge = 19106.1 C)

(a) (i) Calculate the mass, in atomic mass unit, of a neutron. (3 marks)

(ii) The fuel rods in the reactor contain 4100.1 kg of U-235 isotope. Calculate the total

energy released from the complete fission of all the U-235 nuclei in the fuel rods.

(3 marks)

(iii) If the mean power output of the reactor is 500 MW and the efficiency of conversion

of nuclear energy to electrical energy is 40 %, estimate the time for which the fuel

rods can be used. (2 marks)

(iv) Explain why the fuel rods are usually replaced well before the time estimated in (a)

(iii) has elapsed. (2 marks)

(b) In an emergency, explain how the reactor can be shut down immediately. (2 marks)


P.17

17

1997 – 10

In an experiment to investigate the absorption of and rays by materials, a source

emitting and rays is placed at a distance of about 5 cm from a G-M tube as shown in Figure 10.1

Figure 10.1

The count rates, N, are measured for different thickness, d, of absorber plates. The results are shown in

Figure 10.2, with curve A corresponding to the measurements using aluminium absorber plates while

curve B corresponds to those using lead absorber plates.

Figure 10.2

(a) (i) Curve A shows a considerable decreases in count rate up to a thickness of 7 mm; a

further increase in d only results in slight decrease in count rates. Explain why this is

so. (2 marks)

(ii) From the graphs in Figure 10.2, estimate the minimum thickness of lead needed to

absorb most of the rays. (1 mark)

(iii) The source also emits -particles. Explain why their effects ca n be neglected in this

experiment. (1 mark)

1995 – 10

A geologists wants to find the age of a sample of rock containing 40

K which decays to give the stable

isotope 40

Ar. The activity of the sample is found to be 1.6 Bq while the original activity of a similar

rock having the same mass is 4.8 Bq. The half-life of 40

K is 1.3 x 109 years.

(a) (i) Find the decay constant of 40

K. (2 marks)

(ii) Give the physical meaning of the decay constant of a radioactive isotope. (2 marks)

(b) Find the age of the rock sample. (2 marks)

(c) Give two factors that determine the activity of a radioactive source. (2 marks)

(a) The decay of 40

K to 40

Ar is spontaneous. How is the magnitude of the binding energy of 40

K

compared to that of 40

Ar? (2 marks)

(e) Mention a difficulty involved in measuring such a small decay rate of 1.6 Bq. (1 mark)

N/s-1

0

10

20

30

40

50

60

0 2 4 6 8 10 12 14

lead

aluminium

N/s-1

d/mm

(A)

(B)

source

24 days

72 s absorbers

G-M tube


P.18

18

AL93-IIB12

(a) Figure 12.1 shows the decay series for U23592 .

Figure 12.1

(i) Name the particles emitted when Uranium (U) decays to Thorium (Th) and Thorium

(Th) decays to Protactinium (Pa). (1 mark)

:Th U

: PaTh

(ii) Given that the half-life of U23592 is 8101.7 years, what will be the percentage of

U23592 left after 10

8 years? (3 marks)

(b) The following equation represents a possible nuclear reaction in a fission reactor:

n3BaKrnU 10

14256

9136

10

23592

Given : the mass of one nuclide of u 235.0439 U23592 ,

u 0087.1n 10 ,

u 9234.90Kr 9136 ,

u 141.9164Ba14256 ,

unified atomic mass unit kg 1066.1u 1 27 .

(i) According to the above equation, what is the mass defect between the reactants and

products when one U23592 nucleus undergoes fission? (2 marks)

(ii) If 51000.4 kg of U23592 splits per second, calculate the rate of energy production.

(3 marks)

(c) Explain how energy can be extracted from the core of a fission reactor for producing

electricity. (3 marks)

1985 – 7

In a hospital, radioactive waste

produced by iodine-125 is stored in a

special store-room before final disposal.

Batches of waste with activity 100 Ci

are deposited in the store-room regularly

at 30-day intervals. It is found that the

activity of the waste material in the store

builds up gradually at first, but reaches a

steady value later, as shown in Figure 5.

Figure 5

(a) (i) Explain why the activity of the waste material will not increase further even though

new batches are deposited every 30 days.

144

142

140

138

136

134

88 89 90 91 92

U

Th

Pa

Atomic number

Neu

tro

n n

um

ber


P.19

19

(ii) Suppose the half-life of iodine-125 is 60 days, estimate the activity in the store-room

when it reaches a steady value.

(b) After five years, this hospital stops using iodine-125. Before the waste material can be

disposed of it has to be kept until its activity falls to below 3Ci. Calculate the storage period

required.

(c) Iodine-125 nuclides emit low energy gamma-ray photons. Suggest two precautions that

should be taken in handling this kind of radionuclide.

HKAL – PAPER II

2011 – 43

Radioactive nuclides X and Y have half-lives 2 hours and 4 hours respectively. The decay of both

nuclides gives stable daughters. Initially samples P and Q contain equal number of atoms of nuclide X

and nuclide Y respectively. Which statements are correct?

(1) The initial activity of sample P is higher than that of sample Q.

(2) After 8 hours, sample P contains more active nuclei than sample Q.

(3) After 8 hours, the chance of a nucleus of X in sample P decaying in the next minute is greater

than that of a nucleus of Y in sample Q.

A. (1) and (2) only

B. (1) and (3) only

C. (2) and (3) only

D. (1), (2) and (3)

2010 – 42 A cancer research project employs a certain radioactive source having a half-life of 5.3 years. The

source has been prepared for some time. Now the research treatment requires 10 minutes of irradiation

on rats with cancer using the source. If two years later the same source is to be used for this kind of

treatment, estimate the irradiation time required in order to have the same radiation dosage.

A. 13 minutes

B. 15 minutes

C. 18 minutes

D. It cannot be estimated as the time when the source was freshly prepared is not known.

2009 – 44 In -decay a neutron inside the nucleus changes into a proton and an electron is emitted as a -particle.

Radioactive nuclide plutonium Pu24494 becomes lead Pb208

82 after a series of - and -decays.

Throughout the whole process, how many neutrons inside a Pu24494 nucleus have undergone such

change?

A. 3

B. 6

C. 9

D. 12

2007 – 24

A radioactive source consists of 64 1012

atoms of nuclide P of half-life 2 days. Another source

consists of 8 1012

atoms of nuclide Q of half-life 3 days. After how long will the number of active

nuclei in the two sources be equal? (Assume that the daughter nuclides of both P and Q are stable.)

A. 6 days

B. 9 days

C. 12 days

D. 18 days

2006 – 23 Which of the following gives the correct meaning of the decay constant of a radioactive substance?

A. It is the rate of disintegrations of the substance.

B. It is the number of disintegrations of the substance occurring on one half-life of the

substance.

C. It is the fraction of the active nuclei present that decay in one second.

D. It is equal to the reciprocal of the half-life of the substance.


P.20

20

2006 – 24

Some typical radiation doses are tabulated as follows:

Radiation dose

Watch television 0.005 mSv/hr for watching television every day in a year

Flying in an aircraft 0.001 mSv/hr

X-ray check 0.020 mSv each time

Arrange the following in ascending order of total radiation dose in one year.

(1) Watching television for 4 hours every day

(2) Travelling on an aircraft for 10 hours every month

(3) Taking X-ray check every 6 months

A. (1), (2), (3)

B. (2), (1), (3)

C. (1), (3), (2)

D. (3), (1), (2)

2005 – 22

The following equation represents a nuclear fission reaction, producing q neutrons.

nqKrBanU 10

92Z

14156

10

23592

What are the values of the atomic number Z and the number q?

Z q

A. 37 2

B. 36 2

C. 36 3

D. 34 3

2005 – 23

A detector placed near a source of gamma radiation records a count rate of 960 counts per second. The

half-life of the source is 12 hours. A slab of material of thickness 6 cm is then placed between the

source and the detector. The `half-value thickness’ of the material is 2 cm (i.e. the intensity of the

radiation would reduce by half after passing through 2 cm of the material). Estimate the count rate

recorded by the detector after one day. (Neglect any background radiation.)

A. 160 counts per second

B. 80 counts per second

C. 60 counts per second

D. 30 counts per second

2005 – 24

On which of the following does the activity of a radioactive source depend?

(1) the number of active nuclides in the source

(2) the half-life of the source

(3) the nature of the nuclear radiation emitted by the source

A. (1) only

B. (3) only

C. (1) and (2) only

D. (2) and (3) only

2004 – 42 The activity of a freshly prepared sample of

60C is 1.0 x 10

6 Bq. The half-life of

60C

is 5.3 years.

Estimate the number of 60

C nuclei in the sample that decay in the first day.

A. 5.2 x 102

B. 3.2 x 108

C. 8.6 x 1010

D. It cannot be estimated as the initial number of nuclei in the sample is not given.

2004 – 44

The following nuclear reaction represents the two deuterons, H21 , which combine to form a helium

isotope, He32 , with the release of energy.

energy X HeH2 32

21


P.21

21

Which of the following statements are correct?

(1) This is an example of nuclear fusion.

(2) The total mass of He3

2and X is greater than that of the two H2

1 .

(3) X is a neutron.

A. (1) and (3) only

B. (1) and (2) only

C. (2) and (3) only

D. (1), (2) and (3)

2003 – 43 The sun and stars generate their energy mainly by

(1) radioactive decay.

(2) nuclear fission.

(3) nuclear fusion.

A. (1) only

B. (3) only

C. (1) and (2) only

D. (2) and (3) only

2003 – 44

A nuclide in a radioactive sample has a constant chance of 610

1 to decay in one second. What is the

approximate half-life of the sample?

A. 1 day

B. 1 week

C. 1 month

D. 1 year

2003 – 45

The average background count rate, in s-1

, in Hong Kong is of the order of

A. 10-2

.

B. 100.

C. 102.

D. 104.

2001 – 42

The activity of a radioactive sample was 70 Bq at time t = 5 minutes and 49 Bq at t = 10 minutes.

Deduce its activity at time t = 0.

A. 112 Bq

B. 100 Bq

C. 95 Bq

D. 91 Bq

E. 80 Bq

2001 – 45

The table below gives the corrected count rate (in counts per minute) from three samples of radioactive

isotopes at three different times.

Isotope 0 min 20 min 40 min

X

Y

Z

480 243 119

135 32 9

168 118 93

The above data show that

(1) X produces the most penetrating radiation.

(2) Y has the largest decay constant.

(3) Z has the longest half-life.

A. (1) only

B. (3) only


P.22

22

C. (1) and (2) only

D. (2) and (3) only

E. (1), (2) and (3)

2000 – 44

A GM counter is placed close to and in front of a radioactivity source which emits both and

radiation. The count rate recorded is 500 counts per minute while the background count rate is 50

counts per minute. Three different materials are placed in turn between the source and the counter.

The following results are obtained.

Material Recorded count rate / count per minute

(Nil)

Cardboard

1 mm of aluminum

5 mm of lead

500

x

y

z

Which of the following is a suitable set of values of x, y and z?

x y z

A. 350 350 150

B. 350 150 50

C. 350 150 0

D. 150 150 50

E. 150 50 50

2000 – 45

The following equations represent some typical nuclear reactions:-

(I) HeLiHBe 42

63

11

94

(II) nHeHH 10

42

31

21

(III) n3BrLanU 10

8535

14857

10

23592

Which of the following descriptions of these reactions is/are correct?

(1) Reaction (I) represents a spontaneous -decay.

(2) Reaction (II) represents a nuclear fusion.

(3) Reaction (III) represents a chain reaction

A. (1) only

B. (3) only

C. (1) and (2) only

D. (2) and (3) only

E. (1), (2) and (3)

1999 – 43

Carbon-14 is radioactive and undergoes -decay with a half-life of about 5600 years. A GM tube

together with a scalar are used in an experiment to determine the concentration of carbon-14 in piece of

excavated wood. To find an accurate value for the activity of the excavated wood, the experimenter

should

(1) prepare a sample of pure carbon-14 from the piece of excavated wood.

(2) take a count over as long a period of time as possible.

(3) take a second count without the presence of the excavated wood.

A. (1) only

B. (3) only

C. (1) and (2) only

D. (2) and (3) only

E. (1), (2) and (3)

1998 – 41

The activity of a sample of radioactive isotopes decreases to 1/3 of its initial value in 12 s. How much

more time would be required for the activity to decrease to 1/9 of its initial value?

A. 4 s

B. 8 s

C. 12 s

D. 16 s

E. 24 s


P.23

23

1998 – 43

A radioactive sample, initially consists of only nuclide X, decays by the emission of an alpha particle to

form a stable daughter nuclide Y. Which of the following quantities will decrease with time?

(1) The rate of decay of nuclide X.

(2) The rate of growth of nuclide Y.

(3) The rate of emission of alpha particles.

A. (1) only

B. (3) only

C. (1) and (2) only

D. (2) and (3) only

E. (1), (2) and (3)

1998 – 44

When several neutrons and protons come together to form a stable nucleus, which of the following

statements is/are correct?

(1) Energy is released.

(2) The mass of the nucleus is smaller than the sum of the mass of the individual nucleons.

(3) In the nucleus, the electrostatic repulsion between two protons is overcome by the nuclear

force between them.

A. (1) only

B. (3) only

C. (1) and (2) only

D. (2) and (3) only

E. (1), (2) and (3)

1997 – 43

Ra22688 is one of the nuclides in the uranium decay series. If the stable end-product of this series is

Pb20682 , the number of -particles emitted between the Ra226

88 stage and the end of the series is

A. 4

B. 6

C. 10

D. 14

E. 20

1996 – 41

A radioactive source is test as follows:

Absorber placed between

Source and GM tube

Effect on count rate

(1) Thin aluminum foil (0.2 mm)

(2) Thin lead sheet (2 mm)

(3) Thick lead sheet (20 mm)

Fall appreciably.

No significant difference with (1).

Falls below that in (1).

What type(s) of radiation does the source emit?

A. only

B. only

C. only

D. and only

E. and only

1996 – 44

A counter is placed near a very weak radioactive source which has a half-life of 1 hour. The counter

registers 100 counts/min at noon and 80 counts /min at 1 p.m. The expected count rate, in counts/min,

at 3 p.m. on the same day is

A. 40

B. 50

C. 55

D. 60

E. 65


P.24

24

1995 – 44

Rn226

88 decays to Rn222

86 with a half-life of 1 600 years. Which of the following statements is/are

correct?

(1) particle is produced in the decays.

(2) All Rn22288 has decayed after 3 200 years.

(3) The half-life of Rn22688 can be shortened by heating.

A. (1) only

B. (3) only

C. (1) and (2) only

D. (2) and (3) only

E. (1), (2) and (3)

1994 – 44

A detector is used for monitoring an source and a reading of 120 units is observed. After a time equal

to the half-life of the source, the reading has fallen to 64 units. If a 5 mm thick lead sheet is inserted

between the source and the detector, the reading would probably be

A. 0 unit

B. 4 units

C. 8 units

D. 16 units

E. 32 units

1994 – 45

A stationary uranium-238 nucleus undergoes -decay. What is the ratio of the kinetic energy of the

daughter nucleus to that of the -particle?

A. 238:4

B. 4:238

C. 234:4

D. 4:234

E. 1:1

1993 – 47

The diagram shows an alpha-particle ‘colliding’ head-on with an atomic nucleus. At P, the alpha-

particle is at the closest distance ro from the nucleus. Which of the following statements is/are correct?

(1) At P, the electric potential energy of the system is maximum

(2) ro is of the order 10-14

m

(3) ro gives an upper limit for the sum of the radii of the alpha-particle and the nucleus.

A. (1) only

B. (3) only

C. (1) and (2) only

D. (2) and (3) only

E. (1), (2) and (3)

1993 – 48

The number of radioactive nuclides in two different samples P and Q are initially 4N and N

respectively. If the half-life of P is t and that of Q is 2t, the number of radioactive nuclides in P will be

the same as the number of radioactive nuclides in Q after a time of

A. t/2

B. t

C. 2t

D. 4t

E. 8t

1992 – 45

A radioactive source consists of a mixture of two radioisotopes P and Q. P has a half-life of 1 hour and

Q has a half-life of 2 hours. Both P and Q have stable daughter nuclei. The initial activity recorded by

a counter is 600/min. After 4 hours the counter registers an activity of 60 counts per min. What was

the contribution of P to the initial count rate (in counts per min.)?

+ r0

particle

P

atomic nucleus


P.25

25

A. 120

B. 200

C. 360

D. 400

E. 480

1992 – 48

XN protonparticle alpha147

In the above nuclear reaction, X is

A. 178O .

B. 179F .

C. 178N .

D. 116C .

E. 189F .

1990 – 48

A radioactive source is placed in front of a GM tube connected to a counter. Various absorbers are

placed between the source and the GM tube and the count-rate recorded. The following results were

obtained:

Absorber Counts per minute

No absorber 711

A sheet of paper 508

5 mm thick aluminum 493

25 mm thick lead block 218

It can be deduced from these results that the radiation(s) emitted by the source is/are

A. and rays only

B. and rays only

C. rays only

D. rays only

E. rays only

1989 - 46

A neutral particle decays in a short time into a proton and a negative particle. The initial and

subsequent paths of the particles in a magnetic field acting into the plane of the paper are shown above.

Which of the following gives the respective paths for the neutral particle, the proton and the negative

particle?

Neutral particle The proton Negative particle

A. R S T

B. R T S

C. S R T

D. S T R

E. T R S

1989 – 49 A helium atom, a hydrogen atom and a neutron have masses of 4.003 u, 1.008 u and 1.009 u (unified

atomic mass units) respectively. Assuming that hydrogen atoms and neutrons can fuse to form helium,

the binding energy of a helium nucleus is

A. 0.0031 u.

B. 0.031 u

C. 1.017 u.

D. 2.014 u.

E. 2.017 u.

R

S T


P.26

26

1985 – 31 Proactinium extract from a solution of uranyl nitrate decays with a half-life of 72 s. The value of the

decay constant is

A. 3106.9 s.

B. 3106.9 s-1

.

C. 014.0 s.

D. 9.49 s.

E. 9.49 s-1

.

1984 – 33

An alpha particle collides with a stationary helium nucleus ( He42 ) in a cloud chamber. Which of the

following diagrams represents the most probable set of tracks?

A. B. C.

D. E.

1983 – 28

A radioactive source of gamma rays has a half-life of 2 days. A geiger counter placed 3 m from the

source initially has a count-rate of 1440 per minute. After 6 days the counter is moved back to a

distance of 9 m from the source, and its count-rate, in counts per minute, is then

A. 20

B. 60

C. 180

D. 320

E. 360

1982 – 35

A radioactive source with half-life 2/1t initially contains N atoms of the radioactive element. The

energy released in each disintegration is E. What is the total energy relaesed in time 2 2/1t ?

A. NE4

1

B. NE2

1

C. NE4

3

D. 2/12

1NEt

He

He

He

He


P.27

27

1981 – 33

A stationary radioactive nucleus of mass N units emits an alpha particle of mass 4 units, leaving a

residual nucleus of mass ( 4N ) units. The ratio of the kinetic energy of the alpha particle to the

kinetic energy of the residual nucleus is

A. 4

4N

B. 2

2

)4( N

N

C. 2

2)4(

N

N

D. 2

2

4

)4( N

E. 3

3

4

)4( N

1980 – 32

Which of the graphs below correctly represents the variation of the activity X of a radioactive sample

with the number N of undecayed nuclei in the sample?

A. B. C. D. E.

X

N

X

N

X

N

X

N

X

N

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