Question

The half life of radioactive material is 24.1days. How long will a sample take to decay 90% of it

Answer 1

half life period = 0.693/k
24.1 = 0.693/k
k = 0.693/24.1
k = 0.028755
All radioactive decays follow first order kinetics
kt = 2.303*log(100/10)
kt = 2.303
t =2.303/k
t = 2.303/0.028755
t = 80 days

Answer 2

Explanation:

It is given:

Charcoal has the initial activity, which is denoted as A_{0}=15.3A

0

=15.3 disintegrations per minute per gram.

Charcoal has the half-life, T 12=5730T12=5730 years

After a few years, the charcoal’s final activity, A = 12.3 disintegrations per minute per gram

Constant of disintegration,

\lambda=0.693 \mathrm{T} 12=0.6935370 \mathrm{y}-1λ=0.693T12=0.6935370y−1

For the action to attain 12.3 disintegrations per minute per gram, let the time taken by the sample at a time of t year.

Sample’s activity,

A=A O e-\lambda tA=AOe−λt

A=A O e-0.6935730 \times tA=AOe−0.6935730×t

\Rightarrow \mathrm{t}=1804.3 \text { years }⇒t=1804.3 years