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7 May, 04:10

Calculate the wavelength in nanometers of the light emitted by a hydrogen atom when it's electron falls from the n = 7 to the n = 4 principal energy level. Recall that the engergy levels of the H atom are given by En = - 2.18 x 10 to the negative 18 J (1/n to the second power). (c = 3.00 x 10 to to the 8 th power m/s; h=6.63 x 10 to the negative 34 j. s

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  1. 7 May, 06:04
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    2.165 x 10^3 nm.

    Explanation:

    Using Rybergs equation,

    1/lambda = R * (1/n1^2 - 1/n2^2)

    Where,

    R = rybergs constant = 109737.32 cm^-1

    n1 = 7

    n2 = 4

    = 109737.32 * (1/7^2 - 1/4^2)

    = 4619.05

    Lambda = 2.165 x 10^-4 cm

    Since 100 cm = 1m, 1 nm = 10^-9 m

    = 2.165 x 10^-4 cm * 1 m/100 cm * 1 nm/10^-9 m

    = 2.165 x 10^3 nm.
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