Question

If nucleus A has a probability (P) of decaying in time (t) and nucleus B has a probability (2P) of decaying in time (t), which statement is true about the half-lives of nucleus A and nucleus B?

a) The half-life of nucleus A is twice the half-life of nucleus B.
b) The half-life of nucleus B is twice the half-life of nucleus A.
c) The half-life of nucleus A is the same as the half-life of nucleus B.
d) The half-life of nucleus A is (e') × greater than the half-life of nucleus B.

Answer 1

Nucleus B, with a decay probability of 2P, will have a shorter half-life than nucleus A, which has a decay probability of P. Thus, the half-life of nucleus B is twice the half-life of nucleus A.

Step-by-step explanation:

If nucleus A has a probability (P) of decaying in time (t) and nucleus B has a probability (2P) of decaying in time (t), we can deduce the relationship between their half-lives. Since nucleus B has twice the probability of decaying as nucleus A in the same time period, this suggests that it takes a shorter amount of time for half of nucleus B to decay compared to nucleus A. Therefore, the half-life of nucleus B is shorter than that of nucleus A, indicating that the correct statement is (b) The half-life of nucleus B is twice the half-life of nucleus A.