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The half-life of a radioactive substance X is equal to the mean lifetime of another radioactive substance Y. If both substances start with the same number of atoms, then which statement is true?

1. X and Y decay at the same rate throughout
2. X decays faster than Y
3. Y decays faster than X
4. X and Y have the same decay rate only at the beginning

Correct answer: Y decays faster than X

Solution

Mean life tau = 1.44 x half-life. Given T_half(X) = tau(Y), we get T_half(X) = 1.44 x T_half(Y), so Y has the shorter half-life and larger decay constant. Y decays faster than X.

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