Question

Palladium-107 undergoes b decay (t1/2 = 6.5 ´ 105 yr) to form silver-107. How long will it take for 0.150 mol of silver-107 to form from 1.25 mol of palladium-107?

Answer 1

1.2×10^5 years

See the image.

Answer 2

It takes  1.2 * 10^5 years for 0.150 mol of silver-107 to form from 1.25 mol of palladium-107.

• T1/2 = 0.693 / K

K = 0.693 / 6.5 * 10^5    …..(i)

• Nt = 1.25 – 0.150

   = 1.1 mole

• Nt = N0 e^-kt

1.1 = (1.25) e^-kt

0.88 = e^ -kt

ln 0.88 = -kt

0.128 = kt

Putting value of k from (i) ,

0.128 = (0.693 / 6.5 * 10^5 ) * t

t = 1.2 * 10^5 years