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

We need to identify which statement is NOT true for radioactive decay.

Option 1: Decay constant increases with increase in temperature.

Radioactive decay is a nuclear process and is independent of temperature. The decay constant does NOT change with temperature. This statement is NOT TRUE.

Option 2: Amount of radioactive substance remained after three half lives is 1/8th of original amount.

After n half-lives, the remaining amount is $$(1/2)^n$$ of the original. After 3 half-lives: $$(1/2)^3 = 1/8$$. This is TRUE.

Option 3: Decay constant does not depend upon temperature.

This is TRUE as radioactive decay is a nuclear process independent of external conditions.

Option 4: Half life is $$\ln 2$$ times of mean life.

$$t_{1/2} = \frac{\ln 2}{\lambda} = \ln 2 \times \tau$$ where $$\tau = 1/\lambda$$ is the mean life. This is TRUE.

The correct answer is Option 1: Decay constant increases with increase in temperature (this is false).