A sample of a radioactive element whose half-life is 30 s contains a million nuclei at a certain instant of time. How many nuclei will be left after 10 ~s ?

Step-by-step solution

Half-life of radioactive sample, T_ 1 / 2 =30 ~s , N₀=10⁶ If N be the remaining number of nuclei after t=10 ~s , then according to radioactive decay law, aligned N &=N₀ ( 1 2 )^ n =10⁶ ( 1 2 )^ t / T_ 1 / 2 &=10⁶ ( 1 2 )^ 10 30 =10⁶ ( 1 2 )^ 1 / 3 &=10⁶(0.796)=7.96 10⁵ aligned