1. Aim # 26: How do we calculate the rate of radioactive decay?
H.W. # Study pp (sec )
Ans. ques. p. 920 # 24
p. 921 # 31,34,35,39
p.925 # 87

2. A. Positive Ion Bombardment
I Nuclear Transmutation – a change of one kind of nucleus to another, induced by colliding another nucleus (e.g. 4He) or a neutron with it e.g Pu + 4He → 242Cm + 1n
A. Positive Ion Bombardment
239Pu + 4He → 242Cm + 1n (produces Curium)
242Cm + 4He → 245Cf + 1n (produces Californium)

3. 239Np → 239Pu + 0e (produces Plutonium) 93 94 -1
B. Neutron Bombardment U + 1n → 239Pu + 0e (produces Neptunium)
239Np → 239Pu + 0e (produces Plutonium)
239Pu + 21n → 241Pu → 241Am + 0e (produces Americium)

4. Artificially produced elements with atomic numbers above 92 are known as transuranium elements.
II Rates of Radioactive Decay
A. Radioactive decay is a first-order process and has a characteristic half-life.
B. Each isotope has its own characteristic half-life.
C. Half-lives are unaffected by external conditions.
D. Calculations base upon half-life.
1. The rate of decay is given by Rate = -ΔN α N Δt Rate = kN where N is the number of (activity) nuclides in the sample.

5. Rate = -ΔN =kN Δt
ΔN = -kΔt N
Using integral calculus,
ln Nt = -kt N where N0 is the number of nuclides at t= Nt is the number of nuclides remaining at time t
when Nt = ½ N0
ln ½ N0 = -kt1/ N0

6. ln ½ = -kt1/2
t1/2 = -ln ½ k
t1/2 = k where k is the decay constant (measured in disintegrations/unit time)
t1/2 is the half-life

7. Problem: The rate constant for the decay of a certain radioactive nuclide is 1.0 x 10-3 h-1. What is the half-life of this nuclide?
Ans: t1/2 = 0.693/(1.0 x 10-3 h-1) = 693 h
Problem: A sample to be used for medical imaging is labeled with 18F, which has a half-life of 110. min. What percentage of the original activity in the sample remains after 300. min?
Ans: Since activity = kN % activity remaining = kNt = Nt kN0 N0
ln Nt = -kt N0
Nt = e-kt N0

8. k = = 6.30 x 10-3 min min
-(6.30 x 10-3 min-1)(300. min) Nt = e N0
Nt = .151 = 15.1% N0
2. Radioactive Dating The % pf 14C in living organisms is constant, maintained by their intake of carbon from other animals and plants.

9. Plants take in 14C from CO2 in the atmosphere. 14N + 1n → 14C + 1p
When an organism dies, the amount of 14C within it decreases at a rate consistent with its half-life. Working backward, we can determine when the organism died.
Problem: A wooden object from an archeological site is subjected to radiocarbon dating. The activity of the sample due to 14C is measured to be 12.4 disintegrations per second. The activity of a carbon sample of equal mass from fresh wood is disintegrations per second. The half-life of 14C is 5730 y What is the age of the archeological sample?

10. Ans: k = = = 1.21 x 10-4 y t1/ y
ln Nt = -kt N0
19.5 disintegrations/sec = kN0
12.4 disintegrations/sec = kNt
N0 = dis/sec ͘ x 10-4 y-1
Nt = dis/sec ͘
1.21 x 10-4 y-1
t = -1/k ln Nt/N0 = ln 12.4 dis/sec x 10-4y dis/sec

11. t = = y x 10-4y-1
Practice
Zumdahl p. 870 # 28,32,62