What is the wavelength of light emitted electron in a hydrogen atom undergoes transition from an energy level with n is equal to 42 and energy level with n is equal to 2?

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What is the wavelength of light emitted electron in a hydrogen atom undergoes transition from an energy level with n is equal to 42 and energy level with n is equal to 2?

Text Solution

Solution : The `n_(i) = 4 "to" n_(f) = 2` transition will give rise to a spectral line of the Balmer series. The energy involved in the transition is given by the relation, <br> ` E=2.18xx10^(-18[1/(n_(i)^(2))-1/(n_(f)^(2))]` <br> Substituting the values in the given expression of E <br> `E=2.18xx10^(-18)[1/(4^(2))-1/(2^(2))]` <br> ` 2.18xx10^(-18)[(1-4)/16]` <br> `2.18 xx10^(-18)xx(-(3)/16)` <br> `E= -(4.0875xx10^(-19) J)` <br> The negative sign indicates the energy of emission <br> Wavelength of light emitted `(lambda)=(hc)/E` <br>` (since E=(hc/lambda)` <br> Substituting the values in the given expression of `lambda`. <br> ` lambda =(6.626 xx 10^(-34))(3xx10^(8))/(4.0875xx10 ^(-19))` <br> ` lambda = 4.8631xx10^(-7) m` <br> `486.3 xx10^(-9) m ` <br> 486 nm

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