Question

If the half life of a radioactive nucleus is $3$ days, nearly what fraction of the initial number of nuclei will decay on the $3^{rd}$ day?(Given that $\sqrt[3]{30.25}\approx .0.63$)

• A. $0.63$
• B. $0.5$
• C. $0.37$
• D. $0.13$

Answer 1

The correct option is D $0.13$

Fractional Decay on third day

$=\frac{[N_0{e}^{-2/\tau }-N_0{e}^{-3/\tau }]}{n-0}$; where $\tau =t_{1/2}/ln2=3/ln2$

$=e^{-\frac{2in2}{3}}-e^{-in2}$

$=2^{-\frac{2}{3}}-2^{-1}$

$=0.63-0.5=0.13$.