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Question

The electron energy in hydrogen atom is given by E=21.7×1012n2erg. Calculate the energy required to remove an electron completely from n=2 orbit. What is the longest wavelength (in cm) of light that be used to cause this transition?

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Solution

E=21.7×1012n2erg
Electron energy in the 2nd orbit, i.e., n=2,
E2=21.7×101222erg=5.425×1012erg
and E=0
ΔE= Change in energy =EE2=5.425×1012erg.
Thus, energy required to remove an electron from 2nd orbit =5.425×1012erg
According to quantum equation,
ΔE=hcλ
or λ=hcΔE
(h=6.625×1027ergsec;c=3×1010cm/sec)
and ΔE=5.425×1012erg
So, λ=(6.625×1027)×(3×1010)5.425×1012
=3.7×105cm
Thus, the longest wavelength of light that can cause this transition is 3.7×105cm.

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