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# 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. - Physics

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Numerical

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.

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#### 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

Concept: de-Broglie Relation
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