Question

Uranium-232 has a half-life of 68.8 years. After 344.0 years, how much uranium-232 will remain from a 100.0-g sample?

1.56 g
3.13 g
5.00 g
20.0 g

Answer 1

To solve this question first determine the number of half lives have gone by to equal 344 years. Which is 5 half lives. Then starting with 100 grams keep on multiplying by 1/2 or dividing by 2 to obtain the amount after 5 half lives have occurred. The amount that will remain from a 100.0 gram sample is 3.13 grams.

Answer 2

Answer: 3.13 g

Step-by-step explanation:

Radioactive decay follows first order kinetics.

Half-life of uranium-232 = 68.8 years

`\lambda =\frac{0.693}{t_{(1)/(2)}}=(0.693)/(68.8)= 0.010072674 year^(-1)`

`N=N_o* e^(-\lambda t)`

N = amount left after time t

`N_0` = initial amount

`\lambda` = rate constant

t= time

`N_0` = 100 g, t= 344 years,
`\lambda=0.010072674 years^(-1)`

`N=100* e^{- 0.010072674 years^(-1)* 344 years}`

N=3.13g