Which of the following statement is not true for radioactive decay?

<p><strong>Answer: Option B</strong> is not true.</p> <p><strong>Explanation:</strong></p> <p><p><strong>Option A</strong> states that the half‐life $t_{1/2}$ is $\ln 2$ times $\frac{1}{k}$, where $k$ is the decay (rate) constant. </p> <p>$ t_{1/2} \;=\; \frac{\ln 2}{k} \;\;=\;\ln 2 \times \frac{1}{k}. $</p> <p>This is correct.</p></p> <p><p><strong>Option B</strong> states that the decay constant $k$ increases with an increase in temperature. However, for radioactive (nuclear) decay processes, the decay constant is essentially <strong>independent of external factors</strong> such as temperature and pressure. Hence, saying that it increases with temperature is <strong>not true</strong>.</p></p> <p><p><strong>Option C</strong> states that the decay constant does not depend upon temperature, which <strong>is</strong> true for radioactive decay.</p></p> <p><p><strong>Option D</strong> states that the amount of radioactive substance left after three half‐lives is $\tfrac{1}{8}$ of the original. Since one half‐life leaves $\tfrac{1}{2}$ of the sample, three half‐lives leave $\left(\tfrac{1}{2}\right)^3 = \tfrac{1}{8}$. This is correct.</p></p> <p>Therefore, the statement that is <strong>not</strong> true is <strong>Option B</strong>.</p>