Question

A radio-active sample of half-life $10$ days contains $1000x$ nuclei. Number of original nuclei present after $5$ days is

• A. $707x$
• B. $750x$
• C. $500x$
• D. $250x$

Answer 1

The correct option is A $707x$

Given : $N_o=1000x$ $T_{1/2}=10$ days $t=5$ days

Nuclei present after 5 days, $N=N_o$ $exp\left(\frac{-0.693}{T_{1/2}}t\right)$

$\therefore$ $N=1000x\times exp\left(\frac{-0.693\times 5}{10}\right)$

OR $N=1000x\times exp\left(-0.346\right)$

OR $N=1000x\times 0.707$ $⟹N=707x$