Question

The rate of decay of radioactive element at a given instant of time is ${10}^3$ disintegration/sec. If the half life of this element is $1$ second, then the rate of decay after $3$ second will be

• A. $12$ per sec.
• B. $50$ per sec
• C. $500$ per sec
• D. $125$ per sec

Answer 1

The correct option is D $125$ per sec

As, rate of decay $\propto$ number of atoms undecayed $\propto {\frac{1}{2}}^{numberofhalf-life}$

In this case, number of half life is $\frac{3}{1}=3$

So, rate of decay after $3$ seconds is $1000/2^3=1000/8=125persec$