A sample of radioactive substance has $${10^6}$$ nuclei. If half life is $$20$$ seconds, the number of nuclei left in the sample after $$10$$ second is

Solution :
$$\eqalign{ & N = {N_0}{e^{ - \frac{\lambda }{t}}} \cr & = {10^6}{e^{ - \left[ {\frac{{\ln 2}}{{20}} \times 10} \right]}} \cr & = {10^6}{e^{ - \ln \sqrt 2 }} \cr & = \frac{{{{10}^6}}}{{\sqrt 2 }} \cr & = 7.07 \times {10^5} \cr & \approx 7 \times {10^5} \cr} $$