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2 August, 04:08

A particle is confined to the x-axis between x = 0 and x = 1 nm. The potential energy U = 0 inside this region and U is infinite outside. What is the longest possible de Broglie wavelength for the particle?

A. infinite

B. 1 nm

C. 2 nm

D. zero

E. 0.5 nm

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Answers (1)
  1. 2 August, 05:15
    0
    According to heisenberg uncertainty Principle

    Δx Δp ≥ h / 4π, where Δx is uncertainty in position, Δp is uncertainty in momentum.

    Given

    Δx = 1 nm

    Δp ≥ h / 1nm x 4π

    ≥ 6.6 x 10⁻³⁴ / 10⁻⁹ x 4 π

    ≥. 5254 x ⁻²⁵

    h / λ ≥. 5254 x ⁻²⁵

    6.6 x 10⁻³⁴ /. 5254 x ⁻²⁵ ≥ λ

    12.56 x 10⁻⁹ ≥ λ

    longest wave length = 12.56 n m
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