Question

Part A

How many years are required for the amount of krypton-85 in a spent nuclear reactor fuel rod to be reduced by a factor of 1/8? The half-life of krypton-85 is 10.8 years.

Express your answer using three significant figures.

t1/8 = ______ years

Part B

How many years are required for the amount of krypton-85 in a spent nuclear reactor fuel rod to be reduced by a factor of 1/32?

Express your answer using three significant figures.

t1/32 = ______ years

Part C

How many years are required for the amount of krypton-85 in a spent nuclear reactor fuel rod to be reduced by a factor of 1/128?

Express your answer using three significant figures.

t1/128 = ______ years

Answer 1

The half-life of krypton-85 is 10.8 years.

That means, in 10.8 years amount of krypton-85 gets reduced by a factor of 1/2.

Now,

Part A How many years are required for the amount of krypton-85 in a spent nuclear reactor fuel rod to be reduced by a factor of 1/8?

To get reduced to 1/8, it requires 3 half-lifes. i.e. 1/2 * 1/2* 1/2 = 1/8

Therefore, t_1/8 = 3 * 10.8 = 32.4 years.

Part BHow many years are required for the amount of krypton-85 in a spent nuclear reactor fuel rod to be reduced by a factor of 1/32?

To get reduced to 1/32, it requires 5 half-lifes. i.e. 1/2 * 1/2* 1/2 *1/2 * 1/2= 1/32

Therefore, t_1/32 = 5 * 10.8 = 54 years.

Part C How many years are required for the amount of krypton-85 in a spent nuclear reactor fuel rod to be reduced by a factor of 1/128?

To get reduced to 1/128, it requires 7 half-lifes. i.e. 1/2 * 1/2 * 1/2 * 1/2* 1/2 *1/2 * 1/2= 1/128

Therefore, t_1/32 = 7 * 10.8 = 75.6 years

Calculations shall be verified once, logic used is correct.

Hope this helps :)