Paper: CSIR-NET June 2012 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Particle In A Box · Marks: 2 · Difficulty: Medium
The probability of finding the particle in a one dimensional box of length 'L' in the region between $\frac{\mathrm{L}}{4}$ and $\frac{3 \mathrm{L}}{4}$ for quantum number $\mathrm{n}=1$ is
(a)$\frac{1}{2}$
(b)$\frac{1}{2}+\frac{1}{\pi}$
(c)$\frac{1}{2}-\frac{1}{\pi}$
(d)$\frac{2}{3}$
Answer
Answer: B ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
P = (2/L)∫_{L/4}^{3L/4} sin²(πx/L) dx = ½ + 1/π ≈ 0.82.