Question

Suppose the half-life of element k is 20 minutes. if you have a 200 g sample of k, how much of element k will be left after 60 minutes? (do not use significant digits in answering this question).

Answer 1

T=20 min
m₀=200 g
t=60 min

the mass of element through time t is:
m=m₀*2^(-t/T)

m=200*2^(-60/20)=25 g

25 grams of element will be left after 60 minutes

Answer 2

Answer: 25 grams

Explanation:

Radioactive decay follows first order kinetics.

Half-life of element = 20 minutes

$\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{20}=0.035min^{-1}$

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

N = amount left after time t = ?

$N_0$ = initial amount  = 200 g

$\lambda$ = rate constant

t= time  = 60 min

$N=200\times e^{- 0.035 min^{-1}\times 60 min}$

$N=25g$

Thus amount left after 60 minutes will be 25 grams.