Plutonium isotope 239Pu decays by alpha decay with a halflif

Plutonium isotope ²³⁹Pu decays by alpha decay with a half-life of 24100 y. How many milligrams of helium are produced by an initially pure 12.6 g sample of ²³⁹Pu at the end of 19720 y? (Consider only the helium produced directly by the plutonium and not by any by-products of the decay process.)

Number

Solution

N_T = N0 (1/2)^T/T_1/2

WHERE N_T = quantity after T time

N0 = initial quantity=12.6g

T_1/2 = half life = 24100 y

T = given time=19720 y

N_{T =} 7.146g

mass decayed = 12.6 - 7.146 = 5.45 g

plutonium deays to 235U and he whose atomic mass =4

therefore mass of he in 5.45 g = 4/239 x 5.45 =0.09 g