Question

The half-life of a radioactive substance is:

• A. \(0.6931 \times X\)
• B. \(\frac{0.6931}{X}\)
• C. \(\frac{0.6931}{\log 10 2}\)
• D. Average age \(0.6931\)

Hint:

Half-life is the time taken for half the radioactive nuclei to decay.

Answer 1

The Correct Option is B

The half-life \( T_{1/2} \) of a radioactive substance is the time required for half of the radioactive nuclei to decay. It is related to the decay constant \( \lambda \) (here given as \( \lambda = X \)) by the formula: \[ T_{1/2} = \frac{0.6931}{\lambda}. \] This relationship comes from the exponential decay law, where the number of undecayed nuclei decreases as: \[ N = N_0 e^{-\lambda t}. \] At \( t = T_{1/2} \), \( N = \frac{N_0}{2} \), leading to the above formula.