Question

10 g pf radioactive material of half life 15 years is kept in a store for 29 years. the amouny of disintegrated material left is?

Answer 1

N= number of radioactive nuclei.
M = mass of radioactive material.

The formula for radioactive decay is:
               dN/dt = - λ N
$N=N_0 e^{-\lambda t},\ \ \ so,\ M = M_0 e^{- \lambda t}\\\\t=\frac{1}{\lambda}Ln(\frac{M_0}{M})\\\\t=Half-life-period=T_{\frac{1}{2}},\ when\ M=M_0/2\\\\T_{\frac{1}{2}}=\frac{Ln2}{\lambda}\\\\Given\ M_0=10gm,\ T_{\frac{1}{2}}=15yrs,\ \ \ t=29yrs\\\\\lambda*t=\frac{Ln2}{15yrs}*29yrs=1.34\\\\M=10*e^{-1.34} gms=2.62 gms$