Question

Consider radium, which has a half-line of 1620 years. How many atoms of radium will decay in 5 s in 15 g of its sample? Consider the atomic weight of radium to be 226 kg/mol.

Answer 1

$$\Delta N=N_0-N=N_0(1-2^{-t/t_{1/2}})\\ =\frac{m}{\mu}N_A(1-2^{-t/t_{1/2}})$$ $$\Delta N=\frac{15}{226}*6.02*10^{23}(1-2^{-5/(1620*3.15*10^7)})\\ =4.0*10^{22}$$