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Question
When the electron orbiting in hydrogen atom in its ground state moves to the third excited state, show how the de Broglie wavelength associated with it would be affected.
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Solution
The velocity of a electron in a hydrogen atom is given by the relation
`"v"_"n" = "e"^2/(2"n"epsilon_0"n") "so" "v"_"n" ∝ (1)/"n"` ...(i)
and the de Broglie wavelength associated with it is `lambda = "h"/"p" = "h"/"mv"`
So `lambda ∝ (1)/"v"_"n"` ...(ii)
using equation (i) and (ii) `lambda ∝ "n"`
So when electron jump from n = to n = 4 level
`lambda_1/lambda_2 = "n"_1/"n"_2 = (1)/(4)`
`lamda_2 = 4lambda_1`
So the wavelength increases four times.
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