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23 August, 09:33

Two adjacent allowed energies of an electron in a one-dimensional box are 5.4 eV and 9.6 eV.

What is the length of the box?

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  1. 23 August, 10:18
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    E = energy in nth state = 5.4 eV

    E' = energy in (n + 1) th state = 9.6 eV

    L = length of the box

    m = mass of electron = 9.1 x 10⁻³¹ kg

    h = plank's constant = 6.63 x 10⁻³⁴

    Energy in nth state is given as

    E = n²h² / (8 m L²) eq-1

    Energy in (n+1) th state is given as

    E' = (n + 1) ²h² / (8 m L²) eq-2

    dividing eq-1 by eq-2

    E/E' = n² / (n + 1) ²

    inserting the values

    5.4 / 9.6 = n² / (n + 1) ²

    n = 3

    using eq-1

    E = n²h² / (8 m L²)

    inserting the values

    5.4 x 1.6 x 10⁻¹⁹ = (3) ² (6.63 x 10⁻³⁴) ² / (8 (9.1 x 10⁻³¹) L²)

    L = 7.9 x 10⁻¹⁰ m
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