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

Step-by-step explanation:

Radioactive decay follows first order kinetics.

Half-life of element = 20 minutes

`\lambda =\frac{0.693}{t_{(1)/(2)}}=(0.693)/(20)=0.035min^(-1)`

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

N = amount left after time t = ?

`N_0` = initial amount = 200 g

`\lambda` = rate constant

t= time = 60 min

`N=200* e^{- 0.035 min^(-1)* 60 min}`

`N=25g`

Thus amount left after 60 minutes will be 25 grams.