# A radioactive sample decays by $$63$$% of its initial value in $$10s$$. It would have decayed by $$50$$% of its initial value in

#### Correct option is A. $$7s$$

A radioactive sample decays by $$63$$% in $$t=\dfrac{1}{\lambda}$$

Hence $$\lambda=1/10$$

$$N=N_0e^{-\lambda t}$$

$$\dfrac{N_0}2=N_0e^{-0.1t}$$

$$0.1t=ln2$$

$$t=6.93s\approx7s$$