1 Answer

Roshan Mathews · Answer 1 · 2020-01-23T11:35:14+0000

Answer: It will take 3 days for half of a 10 g sample to decay.

Explanation:

Half-life of sample of an isotope X = 3 days

$\lambda=\frac{0.693}{t_{(1)/(2)}}=(0.693)/(3 days)=0.231 day^(-1)$

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

$\lnN=-\lambda t\lnN_o$

Sample decayed =
(N_o)/(2)=(10 g)/(2 g)=5 g

N=
$N^o-\text{sample decayed}=10 g-5 g=5 g$ , time = t

$\ln[5 g]=-0.231 day^(-1)* t\ln[10]$

$\ln[(5)/(10)]=-0.231* t$

$\ln(1)/(2)=-0.693=-0.231* t$

t = 3 days

It will take 3 days for half of a 10 g sample to decay.

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