The half-life of a radioactive element is the time needed for half of the material to decay. You have a certain quantity of a mineral containing two radioactive elements X and Y, whose half-lives are 2 and 3 years, respectively. Also, no physical process can produce elements X or Y.
If today the ratio X:Y (mass/mass) is 8:1, what will it be after 6 years?
A) 2:1
B) 16:1
C) 32:1
D) 1:1
E) 4:1
IMAT 2023 · Question 6
Q6 - Problem solving
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The correct answer is E) 4:1.
In 6 years, X goes through 6/2 = 3 half-lives and Y through 6/3 = 2 half-lives.
X: 8 × (1/2)³ = 1
Y: 1 × (1/2)² = 1/4
So X : Y = 1 : 1/4 = 4 : 1.
Sanity check: X decays faster, so the ratio has to drop from 8:1. That rules out 16:1 and 32:1 without any calculation.
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