Chapter 19

Radioactivity and Nuclear Chemistry

2

GOALS

Types of radioactivityIdentify radioactive nuclidesNuclear equationsBinding energy; per nucleon; unitsKinetics of radioactive decay

3

Facts About the Atomic Nucleus

• Every atom of an element has the same number of protons (+ve)atomic number (Z)

• Atoms of the same elements can have different numbers of neutrons (no charge)

• Isotopes: atoms of the same element, having same atomic number, Z, but different mass number, A (diff no. of neutrons).

• Isotopes are identified by their mass number (A)mass number = number of protons + neutrons

4

Facts About the Atomic Nucleus

• mass number = number of protons + neutrons

neutrons = mass number – number of protons

• The nucleus of an isotope is called a nuclide

• Each nuclide is identified by a symbol

X Element AZ

number massnumber atomic

Nuclide Nuclide SymbolsSymbols

• Boron-10 (Boron-10 (101055B) has 5 p and 5 n B) has 5 p and 5 n

• Boron-11 (Boron-11 (111155B) has 5 p and 6 nB) has 5 p and 6 n

10B

11B

• Oxygen-16 (Oxygen-16 (161688O) has 8 p and 8 n O) has 8 p and 8 n

• Oxygen-17 (Oxygen-17 (171788O) has 8 p and 9 nO) has 8 p and 9 n

• Oxygen-18 (Oxygen-18 (181888O) has 8 p and 10 nO) has 8 p and 10 n

6

The Discovery of Radioactivity• Becquerel discovered that certain minerals were

constantly producing penetrating energy rays he called uranic rays (1896)

Marie Curie discovered 2 new elements (Po, Ra) which also emitted uranic rays.

• Curie changed term uranic rays to radioactivity (present in elements other than uranium).

Some nuclei are unstable; they emit particles and/or electromagnetic radiation spontaneously.

This is radioactivity.

7

Types of Radioactive Rays

• Rutherford discovered there were 3 types of radioactivity;

• 2 additional types were later discovered.

• alpha () & beta () decay, gamma ray (then positron emission, and electron capture.

Another type of radioactivity (nuclear transmutation) results from the bombardment of nuclei (heavy) by neutrons, protons or other nuclei (lighter).

8

Penetrating Ability of Radioactive Rays

0.01 mm 1 mm 100 mmPieces of lead

Particle Symbol Nuclear Symbol

proton p+

neutron n0

electron e-

alpha

beta , -

positron , +9

Important Atomic Symbols

p H 11

11

n10

e01

He α 42

42

e β 01

01

e β 01

01

10

Nuclear Equations• nuclear processes are described using nuclear

equations

• use the symbol of the nuclide to represent the nucleus

• atomic numbers and mass numbers are conserveduse this to predict identity of daughter nuclide if parent and

emitted particle are known

nuclides daughter

He Th U

nuclideparent

42

23490

23892

emitted particle: product

captured particle: reactant

He Th U 42

23490

23892

11

Alpha Emission

• an particle contains 2 protons and 2 neutrons

• most ionizing, but least penetrating

• loss of an alpha particle meansatomic number decreases by 2mass number decreases by 4

Rn He Ra 21886

42

22288

He α 42

42

He Th U 42

23490

23892

12

Beta Emission

• An unstable nucleus emits an electron

• when an atom loses a particle itsatomic number increases by 1mass number remains the same

• in beta decay, a neutron changes into a proton

Pa e Th 23491

01

23490

e β 01

01

If californium-251 decays by successive α, α, β emissions, what nucleus is produced?

a) b) c) d) e)  

24395 Am 243

93 Np

24294 Pu

24494 Pu

24792 Pa

14

Gamma Emission• gamma () rays are high energy photons of light

• least ionizing, but most penetrating

• generally occurs after the nucleus undergoes some other type of decay and the remaining particles rearrange

γ00

00

23490

42

23892 Th He U

15

Positron Emission

• The positron has a charge of +1 and negligible massanti-electron

• when an atom loses a positron from the nucleus, itsmass number remains the sameatomic number decreases by 1

• A positron appears to result from a proton changing into a neutron

Ne e Na 2210

01

2211

e β 01

01

n e p 10

01

11

16

Electron Capture

• occurs when an inner orbital electron is pulled into the nucleus

• no particle emission, but atom changessame result as positron emission

• proton combines with the electron to make a neutron

mass number stays the sameatomic number decreases by one

Tc e Ru 9243

01

9244

e01

n e p 10

11

01

17

Summary of Decay Processes

(Table 19.1; pg 871)

Decay Emission At # Mass #

-2 -4 inc

- +1 0 dec

-ray 0 0 -

-1 0 inc

e-capt X-ray -1 0 inc

Z

N

He42

18

Write the nuclear equation for positron emission from K-40

a) Write the nuclide symbols for both the starting radionuclide and the particle

e positron K 04K 01

4019

b) Set up the equation (emitted particles are products; captured particles are reactants)

X e K AZ

01

4019

c) Determine the mass number and atomic number of the missing nuclide (mass and atomic numbers are conserved)

X e K 4018

01

4019

19

4) Determine the element from the atomic number

Ar e K 4018

01

4019

Write the nuclear equation for positron emission from K-40

Q. In a decay series, U-238 emits 8 alpha particles and 6 beta particles. What nuclide is formed?

? He8 e6 U 42

01

23892

Pb X X He8 e6 U 20682

42

01

23892

Mass dec by 32; charge = +6 & -16

20

Write a nuclear equation for each of the following

electron capture by Be-7

positron emission from N-13

beta emission from Ne-24

alpha emission from U-238

Stability Stability of of NucleiNuclei

- stable isotopes stable isotopes fall in a very fall in a very narrow range narrow range called the island called the island of stability.of stability.

22

What Causes Nuclei to Break Down?

• the particles in the nucleus are held together by a very strong attractive force found in the

nucleus called the strong force

acts only over very short distances

• the neutrons play an important role in stabilizing the nucleus, as they add to the strong force, but do not repel each other like the protons do

23

Neutron to Proton (N/Z) Ratio

• the ratio of neutrons : protons is an important measure of the stability of the nucleus

• if the N/Z ratio is too high (neutron rich) – neutrons are converted to protons via decay

• if the N/Z ratio is too low (proton rich) – protons are converted to neutrons via positron emission or electron capture

or via decay – though not as efficient

24

Valley (Island) of Stability (Plot of # Neutrons vs # Protons)

for Z = 1 20 (H - Ca), stable N/Z ≈ 1

for Z = 20 40, stable N/Z approaches 1.25

for Z = 40 80, stable N/Z approaches 1.5

Heavy nuclei: for Z > 83, there are no stable nuclei

low N/Z

25

Determine the kind of radioactive decay that Mg-22 undergoes

• Mg-22Z = 12 (protons)N = 22 – 12 = 10 (neutrons)

• N/Z = 10/12 = 0.83 • from Z = 1 20, stable

nuclei have N/Z ≈ 1

• Mg-22 has low N/Z; it should convert 1

1p into 10n, therefore

it will undergo positron emission or electron capture

26

Determine the kind of radioactive decay that N-18 undergoes

• N-18Z = 7 (protons)N = 18 – 7 = 11 (neutrons)

• N/Z = 11/7 = 1.57 • from Z = 1 20, stable

nuclei have N/Z ≈ 1

27

Q. Which of the following will undergo beta decay?

16O, 20F, 13N

28

Magic Numbers

most stable when N or Z = 2 (He), 8 (O), 20 (Ca), 28 (Ni), 50 (Sn), 82 (Pb)

besides the N/Z ratio, the numbers of protons and neutrons effects stability

most stable nuclei have even numbers of protons and neutrons

only a few have odd numbers of protons and neutrons

if the total number of nucleons adds to a magic number, the nucleus is more stable (compare # electrons in noble gases)

Binding Energy, EBinding Energy, Ebb

--All atoms are a little lighter than they are really

supposed to be..Missing mass: ∆m = mass defect.

-This missing mass is converted to energy, -This missing mass is converted to energy, and released when 1 mole of atoms is and released when 1 mole of atoms is formed from its subatomic particles formed from its subatomic particles (protons + neutrons + electrons). (protons + neutrons + electrons).

--Energy holds the nucleus together. Energy holds the nucleus together.

Calculating Binding Energy, Calculating Binding Energy, EEbb

Eb is the energy required to separate the nucleus of an atom into protons, neutrons, electrons.

For stability, EFor stability, Ebb > electrostatic repulsive forces > electrostatic repulsive forces

between protons.between protons.

In deuterium, In deuterium, 2211HH

2211H H 11

11p + p + 1100nn EEbb = 2.15 = 2.15 10 1088 kJ/mol kJ/mol 22

11HH

EEbb per mol nucleon per mol nucleon = E = Ebb/2 nucleons/2 nucleons

= 1.08 = 1.08 10 1088 kJ/mol nucleons kJ/mol nucleonsAlso, calc EAlso, calc Ebb per nucleon per nucleon ((6.0226.022 10 102323

nucleons) nucleons)

Calculating Binding Energy, Calculating Binding Energy, EEbb

For deuterium, For deuterium, 2211H: H: 22

11H H 1111p + p + 11

00nn

Actual mass of Actual mass of 2211H = 2.01410 g/mol (given or PT)H = 2.01410 g/mol (given or PT)

Mass of proton = Mass of proton = 1.007825 g/mol1.007825 g/mol

Mass of neutron = Mass of neutron = 1.008665 g/mol1.008665 g/mol

Theoretical mass = Theoretical mass = 2.016490 g/mol2.016490 g/mol

Mass defect (‘missing mass’) = Mass defect (‘missing mass’) = 2.0164902.016490 – –

2.014102.01410

= 0.00239 g/mol= 0.00239 g/mol

Calculate Binding Energy, ECalculate Binding Energy, Ebb

Mass defect Mass defect = 0.00239 g/mol = 0.00239 g/mol

= (0.00239 = (0.002391000) kg/mol1000) kg/mol

= 2.39 = 2.39 10 10-6-6 kg/mol kg/mol From Einstein’s equation: From Einstein’s equation:

EEbb = (∆m)c = (∆m)c22 = 2.39 = 2.39 10 10-6-6 kg kg (3.00 × 10 (3.00 × 1088 m/s) m/s)22

= 2.15 ×10= 2.15 ×101111 kg kgmm22/s/s22 (but 1 kg(but 1 kgmm22/s/s22 = 1 J) = 1 J)

= 2.15 = 2.15 10 101111 J/mol J/mol 1000 J = 2.15 1000 J = 2.15 10 1088

kJ/mol kJ/mol Two nucleons for deuterium, Two nucleons for deuterium, 22

11H: H: 1111p + p + 11

00nn

EEbb /mol nucleon = 1.08 /mol nucleon = 1.08 10 1088 kJ/mol nucleons kJ/mol nucleons

Calculating Binding Energy, Calculating Binding Energy, EEbb

For I-127, For I-127, 1271275353I: 53p + 74n (i.e. 127 nucleons)I: 53p + 74n (i.e. 127 nucleons)

Actual mass of Actual mass of 1271275353I = 126.9045 g/mol (given or PT)I = 126.9045 g/mol (given or PT)

53 protons = 5353 protons = 531.007825 g/mol = 53.41473 g/mol1.007825 g/mol = 53.41473 g/mol

74 neutrons = 74 74 neutrons = 74 1.008665 g/mol = 74.64121 g/mol 1.008665 g/mol = 74.64121 g/mol

Theoretical mass defect = Theoretical mass defect = 128.05594 g/mol128.05594 g/mol

Mass defect = (128.05594 -126.9045) g/mol Mass defect = (128.05594 -126.9045) g/mol

= 1.1514 g/mol= 1.1514 g/mol

= = 1.1514 1.1514 10 10-3-3 kg/mol kg/mol

Calculate Binding Energy, ECalculate Binding Energy, Ebb

EEbb = = 1.1514 1.1514 10 10-3-3 kg/mol kg/mol (3.00 × 10 (3.00 × 1088 m/s) m/s)22

= 1.04 ×10= 1.04 ×101414 kg kgmm22/s/s22 (but 1 kg(but 1 kgmm22/s/s22 = 1 J) = 1 J)

= 1.04 ×10= 1.04 ×101414 J/mol J/mol

Also, can express EAlso, can express Ebb in MeV: 1 MeV = 1.602 ×10 in MeV: 1 MeV = 1.602 ×10-13 -13 JJ

EEbb /nucleon = ? MeV /nucleon = ? MeV

EEbb /mol nucleon = 1.04 ×10 /mol nucleon = 1.04 ×101414 J/ (127 nucleons) J/ (127 nucleons)

= 8.19 ×10= 8.19 ×101111 J J

EEbb /nucleon = 8.19×10 /nucleon = 8.19×101111 J J (6.022 ×10 (6.022 ×102323))

= 1.36 ×10= 1.36 ×10-12-12 J J

35

Plot of Eb vs Mass

-the greater the binding energy per nucleon, the more stable the nucleus is

Nuclear FissionNuclear Fission

TThe splitting of a heavy unstable nucleus he splitting of a heavy unstable nucleus of an of an atom into two or more fragments; Pu, U & atom into two or more fragments; Pu, U & Th!Th!

--induced reaction to produce energy!induced reaction to produce energy!n Kr Ba n U 1

09136

14256

10

23592 3

Energy released Energy released 16,800,000,000 16,800,000,000 kJ/mol kJ/mol (235 g Uranium) (235 g Uranium)

Nuclear FusionNuclear Fusion

Free of long-lived radioactive Free of long-lived radioactive wastewaste..

n2 p2 He2 H6 10

11

42

21

More destructive than fission bombs More destructive than fission bombs (WWII)! (WWII)!

More difficult to achieve. Nuclei must More difficult to achieve. Nuclei must travel at v. large KE’s at each othertravel at v. large KE’s at each other..

Light nuclei fuse to generate Light nuclei fuse to generate heavier nuclei (more stable)heavier nuclei (more stable)

38

Kinetics of Radioactive Decay

0

t

0

t

rate

ratelnt

N

Nln k

k

0.693t1/2

Rate = kN It is a first order processN = number of radioactive nuclei

the shorter the half-life, the more nuclei decay

every second (sample is hot!), the higher the rate

1/2t

timelives-half of no.

0NlntNln t k

39

The half life of Pu-236 is 2.86 years. Starting with a 1.35 mg sample of Pu-236, calculate the mass that will remain after 5.00 years

Concept Plan:

Relationships:

mass Pu-236 = 1.35 mg, t = 5.00 yr, t1/2 = 2.86 yr

mass, mg

Given:

Find:

k

693.0t

21 t

m

mln

0

t k

t1/2 k m0, t mt+

k

693.0t

21

1-yr 3224.0yr 86.2

693.0

t

693.0

21

k

40

Starting with a 1.35 mg sample of Pu-236, calculate the mass that will remain after 5.00 years

units are correct, the magnitude makes sense since it is less than ½ the original mass for longer than 1 half-life

Check:

Solve:

t1/2 k m0, t mt+

-1yr 3224.0k

tN

Nln

0

t k

? N t

yr 00.5yr 2423.0t0t

-1

mg 1.35NN ee k

41

An ancient skull gives 4.50 dis/min∙gC. If a living organism gives 15.3 dis/min∙gC, how old is the skull? 14C-t1/2 = 5730 yr

dis = disintegrations

Solve:

Concept Plan:

Relationships:

ratet = 4.50 dis/min∙gC, ratet = 15.3 dis/min∙gC

time, yr

Given:

Find:

k

693.0t

21 t

rate

rateln

0

t k

t1/2 k rate0, ratet t+

1-4 yr 10902.1yr 7305

693.0

t

693.0

693.0t

21

21

k

k

42

An ancient skull gives 4.50 dis/min∙gC. If a living organism gives 15.3 dis/min∙gC, how old is the skull? 14C-t1/2 = 5730 yr

units are correct, the magnitude makes sense since it is less than 2 half-lives

Check:

Solve:

traterate

ln0

t

k

trate

rateln

0

t k

?yr 10901.2

15.3

4.50ln

t1-4-

gC mindis

gC mindis

43

An artifact containing carbon taken from the tomb of a king of ancient Egypt gave 8.1 dpm/gC. How old is the artifact? Carbon from a living organism gives 15.3 dis/min∙gC; 14C-t1/2 = 5730 yr.

dis = disintegrations

1/20

t

t

t0.693 -

rate

rateln

k1/2t

0.693 trate

rateln

0

t k

trate

rateln

693.0 t

02/1 t

t8.1

15.3ln

693.0

5730 t63599.0

693.0

5730

44

• bombardment of one nucleus with another (2H, 4He, 10B, 12C) causing new atoms to be madecan also bombard with neutrons; protons

• reaction done in a particle accelerator linearcyclotron

Tc-97 is made by bombarding Mo-96 with deuterium, releasing a neutron

n Tc H Mo 10

9743

21

9642

Joliot-Curies

Artificial Nuclear Artificial Nuclear ReactionsReactions

Artificial Nuclear ReactionsArtificial Nuclear Reactions

An example of a n, reaction is production of radioactive 31P for use in studies of P uptake in the body.

3115P + 1

0n 3215P +

Reactions using neutrons are called n, reactions because a ray is usually emitted.

Radioisotopes used in medicine are often made by n, reactions.

Transuranium ElementsTransuranium Elements

Elements beyond 92 Elements beyond 92 (transuranium)(transuranium) made made

starting with an starting with an n, n, reaction reaction

2382389292U + U + 11

00n n 2392399292U + U +

2392399292U U 239239

9393Np + Np + 00-1-1

2392399393Np Np 239239

9494Pu + Pu + 00-1-1

47

Q. 56Fe when bombarded with deuterium, produces 54Mn and one other particle. Write a balanced equation for the reaction & identify the other particle.

5626He + 2

1H 5425Mn + ?

48

Nuclide Half-life Organ/SystemIodine-131 8.1 days thyroidIron-59 45.1 days red blood cellsMolybdenum-99 67 hours metabolismPhosphorus-32 14.3 days eyes, liverStrontium-87 2.8 hours bonesTechnetium-99 6 hours heart, bones, liver,

lungs

Medical Uses of Radioisotopes

49

Nonmedical Uses of Radioactive Isotopes

• smoke detectorsAm-241smoke blocks ionized air, breaks circuit

• insect controlsterilize males

• food preservation• radioactive tracers

follow progress of a “tagged” atom in a reaction

50

• authenticating art object many older pigments and ceramics were made from minerals

with small amounts of radioisotopes

• crime scene investigation• measure thickness or condition of industrial

materialscorrosion track flow through processgauges in high temp processes weld defects in pipelines road thickness

Nonmedical Uses of Radioactive Isotopes