ABC26PH1235 · Quantum Chemistry

Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Quantum Chemistry – General · Exam: NET JUNE 2013 · Marks: 2 · Difficulty: Medium

For the particle-in-a-box problem in $(0, \mathrm{L})$ an approximate wave function is given as $\mathrm{x}(\mathrm{L} / 2-\mathrm{x})(\mathrm{L}-\mathrm{x})$. The average energy E for such a state will obey
(a)$\frac{\mathrm{h}^{2}}{8 \mathrm{mL}^{2}}<\overline{\mathrm{E}}<\frac{\mathrm{h}^{2}}{2 \mathrm{mL}^{2}}$
(b)$\overline{\mathrm{E}}>\frac{\mathrm{h}^{2}}{2 \mathrm{mL}^{2}}$
(c)$\frac{\mathrm{h}^{2}}{4 \mathrm{mL}^{2}}<\overline{\mathrm{E}}<\frac{\mathrm{h}^{2}}{2 \mathrm{mL}^{2}}$
(d)$0<\overline{\mathrm{E}}<\frac{\mathrm{h}^{2}}{8 \mathrm{mL}^{2}}$
Answer
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Explanation
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