Question

A lab technician had a sample of radioactive Americium. He knew it was one of the isotopes listed in the table below but did not know which one. The sample originally contained 0.008 g of the isotope, but 120 minutes later it contained 0.125 mg. Use this information to determine which isotope he had. Explain your answer.

Americium isotope	Approximate half-life
Am-245	2 hours
Am-237	1 hour
Am-246	40 minutes
Am-247	20 minutes

Answer 1

we have:

[A]o = 0.008 g

[A] = 1.25*10^-4 g

t = 120.0 min

use integrated rate law for 1st order reaction

ln[A] = ln[A]o - k*t

ln(1.25*10^-4) = ln(8*10^-3) - k*1.2*10^2

-8.987 = -4.828 - k*1.2*10^2

k*1.2*10^2 = 4.159

k = 3.466*10^-2 min-1

Given:

k = 3.466*10^-2 min-1

use relation between rate constant and half life of 1st order reaction

t1/2 = (ln 2) / k

= 0.693/(k)

= 0.693/(3.466*10^-2)

= 20 min

This is half life for Am-247

Answer: Am-247