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

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. 

Answer 2

Answer: 0.125 grams

Explanation:

Radioactive decay follows first order kinetics.

Half-life of give isotope = 20 minutes

$\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{20}=0.03465min^{-1}$

$N=N_o\times e^{-\lambda t}$

N = amount left after time t= ?

$N_0$ = initial amount  = 1.0 g

$\lambda$ = rate constant

t= time = 1 hour = 60 min

$N=1.0\times e^{- 0.03465mi^{-1}\times 60min}$

N=0.125g

Thus amount left after 1 hour is 0.125 grams