Question

Problem 2. A nuclear power plant produces radioactive waste as a byproduct. One such byproduct is an
isotope of the noble gas Krypton, 36Kr85, which decays via ?- decay with half-life T1/2 = 10.8 yrs. Each decay
releases a ?- particle with energy = 0.240 MeV (on average). This energy is converted into thermal energy as
the particle interacts with the surrounding particles.

SHORT QUESTIONS. 2 pts each.
Identify the following attributes of the daughter product that results from decay of 36Kr85.
A. What is the value of N? (i.e., number of neutrons)
B. What is the value of A? (i.e., mass number)
C. What the name of the element?

PROBLEMS. Show work for parts D and E .

D. (3 pts) Radioactive waste must be safely stored until it is no longer dangerous. At one nuclear plant, waste
containing 1.25 x 10^26 atoms of Kr-85 is placed in a container for storage. How many ?- decays will occur
inside the container during the first year of storage?

E. (3 pts) Averaged over that year, what is the (average) rate of heat production (Watts) inside the container, as
a result of ?- decay of Kr-85?

Answer 1

A. Here, Atomic number = Z = 37

   Mass number = A = 85

   Number of neutrons = A-Z = 85-37 = 48

B. Mass number, A = 85

C. Name of the element = Rubidium

D. Now, T_1/2 = 10.8 years

   Decay constant is given by, L = 0.693 / T_1/2 = 0.693 / (10.8 years)

   The decay equation is => N = N₀ e^-Lt = N₀ e^{-(0.693*t)/T1/2}

Here, N = number of Kr-atoms remaining

N₀ = initial number of Kr-atoms = 1.25 x 10²⁶ (Given)

t = Time taken = 1 year (Given)?

Therefore, N = N₀ e^-Lt = N₀ e^{-(0.693*t)/T1/2} = 1.25 x 10²⁶ x e^-0.693/10.8

= 1.25 x 10²⁶ x 0.9378 = 1.17 x 10²⁶

So, number of Kr-atoms decayed = N₀ - N = (1.25 - 1.17) x 10²⁶ = 0.08 x 10²⁶

   So, number of beta-decays =0.08 x 10²⁶ = 8 x 10²⁴

E. Total heat energy produced = E = 0.240 x 8 x 10²⁴ MeV = 1.92 x 10²⁴ MeV

   Now, 1 eV = 1.6 x 10^-19 J ==> 10⁶ eV = 1 MeV = 1.6 x 10^-13 J

Therefore, Total heat energy produced = E = 1.92 x 10²⁴ MeV = 1.92 x 10²⁴ x 1.6 x 10^-13 J = 3.072 x 10¹¹ J

Total seconds in one year = t = 365 * 24 * 60 * 60 = 31,536,000 sec = 3.1536 x 10⁷ sec

    So,the (average) rate of heat production inside the container, as a result of beta-decay of Kr-85 averaged over that year is = E/t = 3.072 x 10¹¹ J / 3.1536 x 10⁷ sec = 0.974 x 10⁴ Watts = 9.74 x 10³? Watts