Answer:
2.79g of ²⁰⁶Hg you have after 13.3 years
Step-by-step explanation:
Kinetics law of radioactive decay is:
Ln [A] = -kt + ln [A]₀
Where A is amount of atom at time t, k is rate constant and [A]₀ is initial amount of the atom
Computing values of the problem:
[A]₀ = 8.39g
t = 13.3years
k = ln 2 / t(1/2) = ln 2 / 22.3 years = 0.03108 years⁻¹
Rate constant = ln2 / Half-life
Replacing:
Ln [A] = -0.03108 years⁻¹ * 13.3 years + ln [8.39g]
ln[A] = 1.7137
[A] = 5.55g of ²¹⁰Pb still after 13.3 years
That means mass of ²¹⁰ Pb that was converted to ²⁰⁶Hg was:
8.39g - 5.55g = 2.84g of ²¹⁰Pb decay
Moles of Pb = Moles of Hg are:
2.84g Pb * (1mol / 210g) = 0.01352 moles Pb = moles ²⁰⁶Hg.
Mass is:
0.01352 moles ²⁰⁶Hg * (206g / mol) =
2.79g of ²⁰⁶Hg you have after 13.3 years