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22 October, 02:22

Compute the energy separation between the ground and third excited states for an electron in a one-dimensional box that is 5.60 angstroms in length. Express the energy difference in kJ⋅mol-1.

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  1. 22 October, 05:16
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    35.51 * 10^-17 KJ/mol

    Explanation:

    We can calculate this using the Planck's equation:

    E = hc/λ

    Where E is the energy separation

    h is the planck's constant with a value 6.63 * 10^-34 m^2kg/s

    c is the speed of light with value 3 * 10^8m/s

    λ is the wavelength with value 5.60Å. 1 Å = 10^-10 m. Hence, 5.60Å is 0.56 * 10^-9nm.

    We plug the values in the equation:

    E = (6.63 * 10^-34 * 3 x 10^8) / 0.56 * 10^-9 = 35.51 * 10^-17KJ

    for Planck's constant (h) and 3 * 108 m/s for the speed of light (c)

    1 Å = 10-10 m

    λ=Ehc
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