Discussion Forum

A radioactive element has rate of disintegration 10,000 disintegrations per minute at a particular instant. after four minutes it becomes 2500 disintegrations per minute.The decay constant per minute is 

Answer:

Explanation:

Given, N₀ = 10,000 disintegration /min

N=2500 disintegeration/min

 t= 4 min

 From the radioactive  decay law , we have

$\frac{N}{N_{0}}=e^{-\lambda t}$

$\therefore$     $\frac{2500}{10000}=e^{-\lambda\times 4}$

 $\Rightarrow$    $\frac{1}{4}=e^{-4\lambda}\Rightarrow e^{4\lambda}=4$

 $\Rightarrow$    $4\lambda=\log_{e}4\Rightarrow 4\lambda=\log_{e}2^{2}$

 $\Rightarrow$   $4\lambda=2\log_{e}2$

$\lambda=\frac{2}{4}\log_{e}2$

$\therefore$       $\lambda$= $0.5\log_{e}2$