# A radioactive sample decays through two different decay processes α−decay and β−decay. Half-life time for α−decay is 3h and half-life time for β−decay is 6h. What will be the ratio of number of initial radioactive nuclei to the number of radioactive nuclei present after 6h?

#### Here after 6 hr, two half time for α decay and one half time for β decay will occur.

Let initial number of nuclei =N0

After two half time for α decay, number of nuclei =N0/4 and

After one half time for β decay, number of nuclei =N0/42=N0/8

Ratio of number of initial radioactive nuclei to the number of radioactive nuclei present after 6 hr =N0N0/8=8