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16 August, 16:05

Consider a particle in a square well. It has mass m and the length of the box is I. Consider the following situations (1) the particle of mass m in the ground state (2) the particle of mass m in the first excited state (3) a particle of mass m in the ground state (4) a particle of mass m in a box of length 2 (5) a particle of mass m in a box of length 21 in the first excited state Which is the proper order from lowest energy to highest energy? (Use". > to reflect the relative values; for example (1) (3) く (4) 5). 2) Select the correct answer O 1) (2) (3) (4) (5)

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  1. 16 August, 17:41
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    The energy of the particle in a square power well is given by the Schrödinger equation, with

    E₁ = RA (h² / 8m L²) n²

    With h the Planck constant the mass of the particle, L the length of the box and n an integer starting 1

    We find the energy for each situation presented

    1) For the fundamental state n = 1

    E₁ = RA (h / 8m L²)

    2) the first excited state corresponds to n = 2

    E₂ = RA (h / 8m L²) 2²

    E₂ = E₁ 4

    3) E₁ = RA (h / 8m L²)

    4) The length of the box is L = 2L

    E' = RA (h' / 8m (2L) ²)

    E' = RA (h' / 8m L²) Ra ¼

    E' = E₁ / 2

    5) L = 2l first excited state

    n = 2

    E '' = RA (h / 8m (2L) ²2) 2²

    E '' = RA (h ' / 8m (L) ²) 4/2

    E '' = E₁ 2

    All energies are in relation to the fundamental state (E1), milking from least to greatest

    E1 / 2
    4 <3 = 1 <5 <2
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