Question

A radioisotope X has as half-life of $10s$. Find the number of nuclei in the sample (if initially there are $1000$ isotopes which are following from rest from a height of $3000m$) when it is at a height of $1000m$ from the reference plane

• A. $50$
• B. $250$
• C. $290$
• D. $100$

Answer 1

The correct option is B $250$

$S=3000-1000=2000m$
$a=g$
$S=ut+\frac{1}{2}a{t}^2$
$2000=\frac{1}{2}g{t}^2$
$t=20s$
$t_{1/2}=10s$
$\lambda =\frac{ln2}{10}$
$N=N_o{e}^{-\lambda t}$
At $t=20s$
$N=\frac{N_0}{4}=250$