b
(b) \(N = {N_0}{\left( {\frac{1}{2}} \right)^{\frac{t}{{{T_{1l2}}}}}}\)

No of atoms at \(t = 2\,hr\),

\({N_1} = 8 \times {10^{10}}{\left( {\frac{1}{2}} \right)^{\frac{2}{1}}} = 2 \times {10^{10}}\)

No. of atoms at \(t = 4\,hr\),

\({N_2} = 8 \times {10^{10}}{\left( {\frac{1}{2}} \right)^{\frac{4}{1}}} = \frac{1}{2} \times {10^{10}}\)  

No. of atoms decayed in given duration

\( = \left( {2 - \frac{1}{2}} \right) \times {10^{10}} = 1.5 \times {10^{10}}\)