Question

210pb has a half-life of 22.3 years and decays to produce 206hg. if you start with 7.50 g of 210pb, how many grams of 206hg will you have after 17.5 years?

Answer 1

The answer 
the main formula to solve such a problem is given by:

m = m0 x (1/2) ^t /T
where,  
m is the amount of the mass after time t
m0 is the amount of the initial mass 
T is the half-time found by means of the formula   T = log 2  / λ = 22.3  years
at t= 0, m0 = 7.50 g, we can find the valuo of the mass after 17.5 years by applying the formula given above:

m = m0 x (1/2) ^t /T
m0 = 7.50 g, t= 17.5 years, T = 22.3  years

so m=7.50  x (0.5)^17.5 / 22.3=7.50  x (0.5)^0.78 = 4.36 g