Question

Uranium 238 is the most common isotope of Uranium. It has an atomic mass of 238.05 and a half-life of 4.47x109 yrs. Imagine a probe that contains 100 g of 238U . What is the activity of this probe due to the radioactive decay of 238U alone? (c) How many nuclei of 238U will be left in the above probe after 109 yrs?

Answer 1

a)

m = given mass = 100 g

M = atomic mass = 238.05 g

number of moles is given as

n = m/M = 100/238.05 = 0.42

N = number of undecayed atoms = (0.42) (6.023 x 10²³)

T_1/2 = half life = 4.47 x 10⁹ yrs

decay constant is given as

= 0.693/T_1/2 = 0.693/(4.47 x 10⁹) = 1.6 x 10^-10

activity is given as

A = N

A = (1.6 x 10^-10 ) (0.42) (6.023 x 10²³) = 4.05 x 10¹³

c)

N' = N e^-t

N' = (0.42) (6.023 x 10²³) e^{-(1.6 x 10-10 x 109)}

N' = (0.42) (6.023 x 10²³) e^-0.16

N' = 2.2 x 10²³