Practice Problems (Chapter 10): Nuclear Chemistry

CHEM 30A

1. Write the equation for the nuclear reaction described in each of the following processes:

a. Americium-241 (241

Am) undergoes alpha decay (inside a smoke detector)

b. Iodine-131 (131

I) undergoes normal beta decay (used in therapy for hyperthyroidism)

c. Fluorine-18 (18

F) undergoes positron emission (one of the radionuclides used in PET scans)

d. Technetium-99m (99m

Tc) undergoes gamma decay to form 99

Tc (a diagnostic radioactive tracer

used to locate tumors, the “m” indicates a metastable excited nuclear state)

e. Chromium-51 (51

Cr) undergoes electron capture (a diagnostic radioactive tracer used to study

blood)

2. Sulfur-35 (35

S) is a naturally occurring radioactive isotope of sulfur that is produced in the upper

atmosphere. What type of radioactive decay would you expect for this isotope, and why?

3. What type of radioactive decay would you expect for 238

U, and why?

KEY

Normal beta decay (–). Based on the average atomic mass of sulfur from the periodic table,

the most abundant isotope of sulfur is 32

S. 35

S has three additional neutrons, and nuclides with

too many neutrons (above the belt of stability) undergo beta decay.

𝟏𝟑𝟏𝟓𝟑

I 𝟏𝟑𝟏𝟓𝟒

Xe + 𝟎

–𝟏 e

𝟏𝟖𝟗

F 𝟏𝟖𝟖

O + 𝟎+𝟏

e

𝟗𝟗𝒎𝟒𝟑

Tc 𝟗𝟗𝟒𝟑

Tc + 𝟎𝟎

𝟓𝟏𝟐𝟒

Cr + 𝟎

–𝟏 e 𝟓𝟏𝟐𝟑

V

𝟐𝟒𝟏𝟗𝟓

Am 𝟐𝟑𝟕𝟗𝟑

Np + 𝟒𝟐

He

Alpha decay (). Uranium has 92 protons, therefore the nucleus is too large (>83 protons).

Large nuclei undergo a series of decays in which alpha decay allows the nucleus to become

smaller. Decay series also typically include some beta decays (to adjust the neutron/proton ratio),

and gamma decays (to relax from excited nuclear states that occur).

time: to 1 t½ 2 t½ 3 t½ 4 t½ 5 t½ 6 t½ 7 t½

percent: 100% 50% 25% 12.5% 6.25% 3.125% 1.5625% 0.78125%

fraction: 1 1/2

1/4

1/8

1/16

1/32

1/64

1/128

4. How many half-lives must pass before the amount of radioactive material remaining is less than 1%

of the original amount?

5. If an object that was once living died 35,500 years ago, what is the exact percentage of the 14

C

remaining in the sample? (For 14

C: t½ = 5730 yrs)

6. All other factors being equal, circle the one that would be more hazardous for each of the following:

a. A gamma emitter…

b. An ingested…

c. A nuclide with a half-life of…

d. A(n)…

Answer: ___________________

% remaining = (0.5)(t / t ½)

(100%)

% remaining = (0.5)

(35,500 yrs / 5730 yrs) (100%) = 1.36452016 % remaining

1.4 % remaining

Note on Sig Figs:

after the division, the exponent is 6.195462478

and the two significant places after the decimal

become the two significant figures in the answer

Answer: Between _____ and _____ half-lives 6 7

3 ft away

9 ft away

alpha emitter

beta emitter

2 hours

2 minutes

alpha emitter

behind

1 mm of paper

gamma emitter

behind

1 mm of lead