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Question
Answer the following question.
Obtain the expression for the ratio of the de-Broglie wavelengths associated with the electron orbiting in the second and third excited states of the hydrogen atom.
Solution
Second excited state (n = 3)
Third excited state (n = 4)
We know that,
`E = "hc"/λ`
`(13.6)/(n^2) = "hc"/λ`
`(13.6)/("n"^2"hc") = 1/λ`
`λ = ("n"^2"hc")/(13.6)`
Now,
`λ_2/λ_3 = ("n"_2^2"hc")/(13.6) xx (13.6)/("n"_3^2"hc")`
`λ_2/λ_3 = ("n"^2 2)/("n"^2 3) = (3)^2/(4)^2`
`λ_2/λ_3 = (9)/(16)`
`λ_2 : λ_3 = 9: 16`
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