Decay of radium-228

Problem statement

Question 4.B.- In the first step of the decay process, each nucleus of the isotope ${}^{228}\mathrm{Ra}$ transmutes into a nucleus of the isotope ${}^{228}\mathrm{Ac}$ and a $\beta^-$ particle is emitted. If you have a 30 g sample of ${}^{228}\mathrm{Ra}$ whose initial activity is $3.03\cdot10^{14}$ Bq, determine:

a) (0.5 marks) The number of $\beta^-$ particles per second that the ${}^{228}\mathrm{Ra}$ sample initially emits.

b) (1 mark) The decay constant and the half-life.

c) (1 mark) The mass of the ${}^{228}\mathrm{Ra}$ isotope that will have been transformed into ${}^{228}\mathrm{Ac}$ after 10 years.

Data: Avogadro's number, $N_A=6.02\cdot10^{23}\ \text{mol}^{-1}$; atomic mass of the ${}^{228}\mathrm{Ra}$ isotope, $M=228$ u.

Source: Madrid university entrance exam (PAU, Spain) · 2025-2026 · Ordinary session · Physics · Question 4.B. Official exam set by the public universities of the Community of Madrid, to whom it belongs; translated from Spanish and reproduced with its source in order to explain it for teaching purposes.