Element X decays to element Y via beta decay with a half-life of 0.77 s.Initially there is a sample of pure X and after 2.31 s there are 7 g of Y.What was the mass of the original sample?

Question

Quizplus · Accepted Answer

First, we can determine how many half-lives have passed by dividing the total time (2.31 s) by the half-life (0.77 s):

2.31 s ÷ 0.77 s/half-life = 3 half-lives

This means that the initial amount of X has been reduced by a factor of 2^3 = 8. So if we call the initial mass of X "m", then:

7 g (final mass of Y) = m/8

m = 56 g

Therefore, the initial mass of the sample was 56 g, and the best choice is C.

Element X Decays to Element Y Via Beta Decay with a Half-Life