Question

2g of Na decay wit a half-life of 15hrs by emitting beta particles, what is the ddecay constant?, average life and activity of the sample

Answer 1

The decay constant of a substance is given by the equation \[\lambda=\frac{\ln2}{t_{1/2}}\] and so for a half life of 15 hours = 15x60x60 seconds we get that \(\lambda=0.0000128\) per second or 0.0462 per hour. Hence the mean life time \((\tau\)) will be the reciprocal of the decay constant, or \[\tau=\frac{1}{\lambda}\], thus the mean life time will be \(\tau=21.64\) hours, or \(77905.53\) seconds.

the activity \(A\) in decays per second is given by \[A=\lambda N_0\] where \(N_0\) is the number of atoms in the sample. The number of atoms in 2 grams of Sodium (Na) is given by \[\frac{2}{23}\times 6.022\times10^{23}\] and hence the activity is
\[A=0.0000128\times\frac{2}{23}\times 6.022\times10^{23}\] meaning that \(A=6.703\times10^{17}\) Bq, where Bq is the unit of Becquerels, equal to 1 decay per second.