Question

A radio isotope X has a half life of $10s$. Find the number of active nuclei in the sample (if initally there are $1000$ isotopes which are falling from rest from a height of $3000m$) when it is at a height of $1000m$ from the reference plane:

• A. $50$
• B. $250$
• C. $29$
• D. $100$

Answer 1

The correct option is B $250$

Time taken in falling a height $h=3000-1000=2000m$

is given as $t=\sqrt[2]{2\frac{2h}{g}}$

putting $g=10,h=2000$ we get $t=20second$

number of half life in this time period is $n=20/10=2$

So number of active nuclei$=initial/2^n=initial/2^2=inital/4=1000/4=250$

Option B is correct.