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16 February, 04:18

The energy required to ionize a mole of potassium ions is 419 kJ/mol. What is the longest wavelength of light capable of this ionization?

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  1. 16 February, 07:07
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    First divide the ionization energy by Avogadro's number to get the energy per atom of potassium;

    419 kj/mol / 6.023 x 10²³

    = 4.19 x 10⁵ / 6.023 x 10²³ = 6.96 x 10⁻¹⁹

    E = hc/λ

    where lambda (λ) is the wavelength, h is Planck's constant, c is the speed of light

    E = 6.96 x 10⁻¹⁹ j/atom

    h = 6.63x10⁻³⁴ Js

    c = 3 x 10 ⁸ m/s

    λ = ?

    λ = hc/E = (6.63x10⁻³⁴ x 3 x 10⁸) / 6.96 x 10⁻¹⁹ = 285.8nm = 286nm

    The longest wavelength of light capable of this ionization is 286nm.
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