For a particle of mass m confined in a box of length L, assume Δ x=L. Assume further that Δ p(min)= p²1/2. Use the uncertainity principle to obtain an estimate of the energy of the particle. The value will be

(b) (ħ²)/(8 m L²). Explanation: Δp ≥ ħ/(2Δx) = ħ/2L; E = ⟨p²⟩/2m ≈ (ħ/2L)²/2m = ħ²/8mL² (b).

For a particle of mass m confined in a box of length L, assume Δ x=L. Assume further that Δ p(min)= p²1/2… · ABC26PH0156

Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Particle In A Box · Exam: CSIR NET 2014 · Marks: 2 · Difficulty: Medium

For a particle of mass $m$ confined in a box of length $L$, assume $\Delta x=L$. Assume further that $\Delta p(\text{min})=\langle p^{2}\rangle^{1/2}$. Use the uncertainity principle to obtain an estimate of the energy of the particle. The value will be

(a)$\frac{h^{2}}{8 m L^{2}}$

(b)$\frac{\hbar^{2}}{8 m L^{2}}$

(c)$\frac{h^{2}}{32 m L^{2}}$

(d)$\frac{h^{2}}{2 m L^{2}}$

Answer

Answer: B ✓ checked by 4AB · confidence medium

Explanation

Δp ≥ ħ/(2Δx) = ħ/2L; E = ⟨p²⟩/2m ≈ (ħ/2L)²/2m = ħ²/8mL² (b).

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