1.

In Bohr's theoryof hydrogenatom ,calculate theenergy of thephoton emitted duringa transitionof theelectron from thefirstexcitedstateto itsground state . Writein whichregionof the electromagneticspectrum thistransition lies . Given Rydbergyconstant R = 1.03 xx 10^(7) m^(-1) .

Answer»

Solution :When in a hydrogen atom a transition takes place from the first excited state (n = 2) to its GROUNDSTATE (n = 1), we have
` (1)/(lambda) = R [(1)/((1)^(2)) - (1)/((2)^(2))] = (3R)/(4)`
`therefore ` Energyof photon`E= hv = (hc)/(lambda) = (hc.3R)/(4) J = (3hcR)/(4 e)eV`
`rArr "" E= (3xx 6.63 xx 10^(-34) xx 3xx 10^(8) xx 1.03 xx 10^(7))/(4 xx 1.6 xx 10^(-9)) eV = 9.6 eV`
The transition lies in the ULTRAVIOLET region of electromagnetic spectrum and corresponds to first line of Lyman series.


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