JEE Main 2025 · 22 January · morning · Single correct · +4 / −1
Which of the following statement is not true for radioactive decay?
- (a) Half life is ln 2 times of 1/(rate constant).
- (b) Decay constant increases with increase in temperature.
- (c) Decay constant does not depend upon temperature.
- (d) Amount of radioactive substance remained after three half lives is 1/8 th of original amount.
Answer and solution
Answer (b) Decay constant increases with increase in temperature.
Solution
Chemistry ma’am · 3 steps
Radioactive decay happens inside the nucleus, so heating the sample cannot speed it up.
- Where decay happens. Radioactive decay is a nuclear process. Temperature only changes how fast atoms and molecules move, and that energy is far too small to disturb a nucleus.
- Check each statement. Test each option against first-order decay and the temperature-independent decay constant λ.
Option What it says Check (a) t_(1/2) = ln 2 × 1/λ True: t_(1/2) = 0.693/λ (b) λ rises with temperature False: nuclear decay ignores temperature (c) λ does not depend on temperature True (d) 1/8 left after 3 half-lives True: (1/2)³ = 1/8 - So. The statement that is not true is (b). The decay constant stays the same at any temperature.
The idea to keep. Radioactive decay is first order and its rate constant is fixed by the nucleus alone. Temperature, pressure and chemical state do not change it.
Answer from the NTA final answer key. Solution by PrepWiser.