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What is the energy in joules required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state ? The ground state energy is `-2.18xx10^(-11)` ergs.

Answer» As ground state electronic energy is `-2.18xx10^(-11)` ergs, this means that `E_(n)=-(2.18xx10^(-11))/n^(2)` ergs
`DeltaE=E_(5)-E_(1)=2.18xx10^(-11) (1/1^(2)-1/5^(2))=2.18xx10^(-11) (24/25)=2.09xx10^(-11)` ergs
`=2.09xx10^(-18)J (1 erg =10^(-7) J)`
When electron returns to ground state (i.e., to `n=1`), energy emitted `=2.09xx10^(-11)` ergs.
As `E=hv=hc/lambda or lambda=(hc)/E=((6.626xx10^(-27)" erg sec")(3xx10^(10)" cm s"^(-1)))/(2.09xx10^(-11) ergs)`
`=9.51xx10^(-6) cm=951xx10^(-8) cm=951 Å`


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