Consider an electron me=9.1 × 10⁻³¹ kg having energy 13.6 eV, confined in an infinite potential well. If the… · ABC26PH1168

Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Quantum Chemistry – General · Exam: CSIR NET 2020-2021 · Marks: 2 · Difficulty: Medium

Consider an electron $\mathrm{m}_{\mathrm{e}}=9.1 \times 10^{-31} \mathrm{kg}$ having energy 13.6 eV , confined in an infinite potential well. If the potential energy inside the well is zero, the expectation value for the square of the electron speed, $\left\langle\mathrm{v}^{2}\right\rangle$ , is

(a)$3 \times 10^{12} \mathrm{m}^{2} \mathrm{s}^{-2}$

(b)$4.3 \times 10^{18} \mathrm{m}^{2} \mathrm{s}^{-2}$

(c)$4.7 \times 10^{12} \mathrm{m}^{2} \mathrm{s}^{-2}$

(d)$4.7 \times 10^{31} \mathrm{m}^{2} \mathrm{s}^{-2}$

Answer

Answer: C ✓ checked by 4AB · confidence high

The source book printed no answer; this one was worked out and checked — see the explanation.

Explanation

With V = 0 inside the box the energy is all kinetic: ⟨v²⟩ = 2E/m = 2 × 13.6 × 1.6×10⁻¹⁹/9.1×10⁻³¹ = 4.8×10¹² m² s⁻².

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