Half life of radio-active element is 1600 years. The fraction of sample remains undecayed after 6400 years…
Half life of radio-active element is 1600 years. The fraction of sample remains undecayed after 6400 years will be
$\frac{1}{16}$
$\frac{1}{4}$
$\frac{1}{8}$
$\frac{1}{24}$
Solution
$\frac{\mathrm{N}}{\mathrm{N}_0}=\left(\frac{1}{2}\right)^{\frac{\mathrm{t}}{\mathrm{T}}}$
Here, $\mathrm{t}=6400$ years and $\mathrm{T}=1600$ years $\therefore \quad \frac{\mathrm{N}}{\mathrm{N}_0}=\left(\frac{1}{2}\right)^{\frac{6400}{1600}}=\left(\frac{1}{2}\right)^4=\frac{1}{16}$