Question

the half life of an isotope X is 3 days how long will it take for 1/2 of a 10 G sample to decay

Answer 1

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

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

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

$\lnN=-\lambda t\lnN_o$

Sample decayed = $\frac{N_o}{2}=\frac{10 g}{2 g}=5 g$

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

$\ln[5 g]=-0.231 day^{-1}\times t\ln[10]$

$\ln[\frac{5}{10}]=-0.231\times t$

$\ln\frac{1}{2}=-0.693=-0.231\times t$

t = 3 days

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