Paper: CSIR-NET June 2011 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Quantum Chemistry – General · Marks: 2 · Difficulty: Medium
For a certain particle encountering a barrier, the tunneling probability is approximately $\mathrm{e}^{-10}$. If the mass is halved and width of the barrier (rectangular) doubled, approximate value of the tunnelling probability will be
(a)$e^{-10/\sqrt{2}}$
(b)$e^{-10\sqrt{2}}$
(c)$e^{-20\sqrt{2}}$
(d)$e^{-10}$
Answer
SELF-PRACTICE — the source book printed no answer.
Nothing is invented here, so this question has no answer on record.
Explanation
Answer: ≈ e^(−10√2) ≈ e^(−14.1) — T ≈ exp[−2a√(2m(V−E))/ħ], so the exponent scales as a√m: 2 × √(1/2) = √2. The exponent becomes 10√2 ≈ 14.1.