1. CHAPTER 28 Nuclear Chemistry
Radioactive Decay

2. Nuclide = atom of an isotope
A. Nuclear Stability
Nuclide = atom of an isotope

3. A. Nuclear Stability
Nuclear stability – stable nuclei always have at least as many neutrons as protons.

4. A. Nuclear Stabiity
For an odd/even or even/odd nucleus, if the mass number is different by more than 1 amu from the rounded atomic mass, the nuclide is unstable.
Ex:

5. A. Nuclear Stability
For an even/even nucleus, if the mass number is different by more than 3 amu from the rounded atomic mass, the nuclide is unstable.
Ex:

6. A. Nuclear Stability
For odd/odd nuclei, only four stable isotopes are found in nature:

7. B. Nuclear Decay 2+ 1- 1+ Alpha particle () helium nucleus
paper 2+
Beta particle (-)
electron 1-
lead
Positron (+)
positron 1+
concrete
Gamma ()
high-energy photon

8. B. Nuclear Decay Top and bottom numbers must balance!! Alpha Emission
parent
nuclide
daughter
nuclide
alpha
particle
Top and bottom
numbers must balance!!

9. B. Nuclear Decay
Beta Emission
electron
Positron Emission
positron

10. B. Nuclear Decay Electron Capture electron Gamma Emission
Usually follows other types of decay.
Transmutation
Atom of one element changes into an atom of another element.

11. B. Nuclear Decay Why nuclides decay…
need stable ratio of neutrons to protons
DECAY SERIES TRANSPARENCY

12. C. Half-life Half-life (t½)
Time required for half the atoms of a radioactive nuclide to decay.
Shorter half-life = less stable.

13. C. Half-life
mf: final mass
mi: initial mass
n: # of half-lives

14. C. Half-life t½ = 5.0 s mf = mi (1/2)n mi = 25 g mf = (25 g)(0.5)12
Fluorine-21 has a half-life of 5.0 seconds. If you start with 25 g of fluorine-21, how many grams would remain after 60.0 s?
GIVEN:
t½ = 5.0 s
mi = 25 g
mf = ?
total time = 60.0 s
n = 60.0s ÷ 5.0s =12
WORK:
mf = mi (1/2)n
mf = (25 g)(0.5)12
mf = g

15. C. Half-life
Nt: final mass
N0: initial mass
t: elapsed time

16. C. Half-life
k: rate constant
t1/2: half-life

17. C. Half-life t½ = 11.4 days k = 0.693 / t1/2 k = 0.693 / 11.4 days
A sample of radium-223 has a half-life of 11.4 days. What is the rate constant for this isotope?
GIVEN:
t½ = 11.4 days
WORK:
k = / t1/2
k = / 11.4 days
k = days -1

18. C. Half-life k = 0.035 yr -1 k = 0.693 / t 1/2 t ½ = 0.693 / k
The rate constant for gold-200 is /year. What is the half-life of gold-200?
GIVEN:
k = yr -1
WORK:
k = / t 1/2
t ½ = / k
t ½ = / yr -1
t ½ = yr ≈ 20. years

19. C. Half-life t ½ = 1.7 x 107 yr ln (N0/Nt) = kt N0 = 3.75 g
The half-life of iodine 129 is 1.7 x 107 years. If a nuclear bomb explosion resulted in 3.75 g of iodine-129, how much time would have to elapse for the amount of iodine-129 to be 0.75 g?
GIVEN:
t ½ = 1.7 x 107 yr
N0 = 3.75 g
Nt = 0.75 g
t = ?
WORK:
ln (N0/Nt) = kt
ln (3.75/0.75) = 0.693/1.7 x 107 t
t = 3.9 x 107 years
(39, 000, 000 years!)

20. D. Radiocarbon Dating
Carbon-14 is in all living things through the carbon cycle.
Amount of carbon-14 stays constant until organism dies, then it begins to decay.

21. D. Radiocarbon Dating
Amount of carbon-14 can be expressed as either a percentage or as a decimal number.
Example: amount of carbon-14 in a dead tree could be expressed as 38% or 0.38 of the original amount.

22. Half-life of carbon-14 : 5730 years
D. Radiocarbon Dating
Half-life of carbon-14 : years

23. D. Radiocarbon Dating
The remnants of an ancient canoe are found in a cave in northern Australia. The amount of carbon-14 is 6.28 counts per minute, and the amount of carbon-14 in a tree today is 13.6 counts per minute. What is the approximate age of the canoe?

24. D. Radiocarbon Dating t ½ = 5730 yr k = 0.693 / 5730 yr
GIVEN:
t ½ = 5730 yr
N0 = 13.6 cts/min
Nt = 6.28 cts/min
t = ?
WORK:
k = / 5730 yr
k = x 10-4 yr -1
ln (N0/Nt) = kt
ln (13.6/6.28) = x 10-4 t
t = years
2011 – 6390 = 4379 BC

25. E. Fission
Occurs when isotopes are bombarded with neutrons and split the nucleus into smaller fragments, accompanied by the release of neutrons and a large amount of energy. (Each atom can capture 1 neutron.)

26. E. Fission
Chain reaction – occurs when atomic nuclei that have split release energetic neutrons that split more nuclei.

27. E. Fission Two steps in controlling fission:
Neutron moderation – water or carbon slows down the neutrons
Neutron absorption – decreases the number of slow neutrons through the use of control rods made of neutron-absorbing materials (usually cadmium)

28. F. Fusion
Occurs when two light nuclei combine to produce a nucleus of heavier mass, accompanied by the release of a large amount of energy.

29. F. Fusion Occurs in all stars
High temperatures are necessary to initiate fusion (no cold fusion yet)
Possible future energy source
Hydrogen bomb is a fusion reaction (fusion of two deuterium nuclei).

30. G. Methods of Detection Geiger Counters (primarily beta)
Scintillation counter – coated screen detects radiation particles.
Film badge – several layers of photographic film encased in a holder. Detects beta and gamma.

31. H. Radioisotopes in Medicine
X-rays: Useful in imaging soft-tissue organs.
Tracers: Iodine-131 is used to check for thyroid problems
Radiation treatment: Some cobalt isotopes are used as radiation sources to treat cancer.