Question

The half-life of a radioactive isotope is 20.0 minutes. What is the total amount of a 1.00-gram sample of this sample of this isotope remaining after 1.00 hour?

Answer 1

Answer: 0.125 grams

Step-by-step explanation:

Radioactive decay follows first order kinetics.

Half-life of give isotope = 20 minutes

`\lambda =\frac{0.693}{t_{(1)/(2)}}=(0.693)/(20)=0.03465min^(-1)`

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

N = amount left after time t= ?

`N_0` = initial amount = 1.0 g

`\lambda` = rate constant

t= time = 1 hour = 60 min

`N=1.0* e^{- 0.03465mi^(-1)* 60min}`

N=0.125g

Thus amount left after 1 hour is 0.125 grams

Answer 2

The amount remaining is obtained using the half life data. The total amount remaining after one hour is equal to 1/( e^ (ln2/(20/60))*1). The final answer is 0.125 grams.