Question

A solution contains 1 billion P atoms (T1/2 of P is 14.3 yrs and it Bdecays with a maximum energy of 1.71 MeV to S) (a) What is the activity in bequerels? (b) How many atoms of phosphorus and of sulfur are there after 1 week? (c) How long will it take for only 100 32P atoms to remain? (d) When will there be no 3P atoms left?

Answer 1

(a)

$A=\lambda N=\frac {N\ln 2}{T_{1/2}}=\frac {10^9\cdot \ln 2}{14.3\cdot 365\cdot 24\cdot 3600}\: Bq= 1.54\: Bq$

(b)

$N=N_0e^{-\lambda t}=10^9\cdot e^{-\frac {7\cdot 24\cdot 3600\ln 2}{14.3\cdot 365\cdot 24\cdot 3600}}= 9.99\times 10^8\: atoms$

(c)

$100=10^9\cdot e^{-\frac {t\ln 2}{14.3\cdot 365\cdot 24\cdot 3600}}$

$t=230.48\: yr$

(d)

$t=\infty$