Question

A sample of a radioisotope shows an activity of 999 disintegrations per minute due to beta decay. If after 1.10 years the activity is 952 disintegrations per minute, what is the half-life of this radioisotope?

Answer 1

15.8 year

Step-by-step explanation:

This this a first order decay reaction first order decay reaction is that reaction in which the rate of reaction is linearly depend on the concentration of reactants. for the first order decay the equation is given as

`ln(A)/(A_0)`= -Kt

where
`A_0`=initial activity and A is the activity at time t K is a rate constant

using above equation
`ln(952)/(999)`= -K×1.10

K=0.043809 /year

Half life=
`(ln2)/(K)`

=
`(ln2)/(0.043809)`

=15.8 year