Question

1. An isotope of radon has a half-life of 14 days. A child goes to visit Grandma in Northern Ontario. While playing in the basement, the child breathes in 4,800 atoms of radioactive radon. Assuming that all of the radon decays in the child lungs, how many weeks will it take until there are only 75 atoms of the isotope left?

Answer 1

Given:

Half life of radon t1/2 = 14 days

Initial # atoms of radon, N(0) = 4800

# atoms left after a certain time (Nt) = 75

To determine:

The decay time (t)

Explanation:

The radioactive decay is given by the following equation:-

N(t) = N(0)exp(-kt) -------(1)

where, the exponential decay constant k is given as:

k = 0.693/t1/2 ----(2)

Based on the given data:

k = 0.693/14 = 0.0495 day⁻¹

Substituting k in eq(1)

75 = 4800 exp(-0.0495t)

ln(75/4800) = (-0.0495t)lne

t = 84 days

1 week = 7 days

therefore, 84 days corresponds to: 84 days * 1 week/7 days = 12 weeks

Ans: It will take 12 weeks for the decay of radon from 4800 to 75 atoms