Tritium has a half-life of 12.3 years.How many years will elapse when the radioactivity of a tritium sample diminishes to 30% of its original value?
A) 29 years
B) 21 years
C) 86 years
D) 57 years

Question

Quizplus · Accepted Answer

We can use the following formula to solve this problem:

Radioactivity = Initial Radioactivity x (1/2)^(time/half-life)

Let t be the time elapsed when the radioactivity diminishes to 30% of its original value. Then we have:

0.3 = 1 x (1/2)^(t/12.3)

Taking the logarithm of both sides, we get:

log(0.3) = log(1) - (t/12.3) x log(2)

Solving for t, we get:

t = -12.3 x log(0.3) / log(2) ≈ 20.9 years

Therefore, the best choice is B) 21 years.

Tritium Has a Half-Life of 12