Question

Consider the decay scheme RaE + (β) → RaF + (β) → RaG (stable). A freshly purified sample of RaE weighs 5×10⁻¹⁰ g at time t = 0. If the sample is undisturbed, calculate the time at which the greatest number of atoms of RaF will be present and find this number. Derive any necessary formula [Half life of RaE (²¹⁰ ₈₃Bi) = 5.0 days; Half life of RaF (²¹⁰ ₈₄ Po) = 138days]

Answer 1

RaE → RaF → RaG 

The rate of decay of RaE is given by 

dN_E/dt = −λENE (1) 

where N_E is the number of atoms of RaE and λE its decay constant. 

The net change of RaF is given by 

dN_F/dt = λ_EN_E − λ_FN_F (2) 

The first term on the right side represents the rate of increase of RaF (Note the positive sign) and the second term, the rate of decrease (Note the negative sign). Here N_E and N_F are the number of atoms of E and F respectively at time t.