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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. - Physics

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Short Note

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.

Concept: Bohr'S Model for Hydrogen Atom
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