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?

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