Question

The rate of decay of a radioactive element at any instant is ${10}^3$ disintegrations $s^{-1}$. If the half-life of the elements is $1s$, then the rate of decay after $1s$ will be

• A. $500s^{-1}$
• B. $1000s^{-1}$
• C. $250s^{-1}$
• D. $2000s^{-1}$

Answer 1

Answer: (A)

$500s^{-1}$

By definition of half life:
Half-life ($t_{1/2}$) is the amount of time required for the amount of something to fall to half its initial value.
Also, by first order decay:
$\frac{dN}{dt}=-\lambda N$
After $t_{1/2}=1s$, both the no. of nuclei and the decay rate will also be half of the initial value
$=0.5\times 1000=500s^{-1}$