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Structure Of Atom

Question
CBSEENCH11005285

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 electron energy is - 2.18 X 10-11 ergs

Solution

As ground state, electronic energy is negative 2.18 space cross times space 10 to the power of negative 11 end exponent space ergs comma space space then
            straight E subscript straight n space equals space fraction numerator negative 2.18 space cross times space 10 to the power of negative 11 end exponent over denominator straight n squared end fraction space ergs
increment straight E space equals space straight E subscript 5 space minus space straight E subscript 1 space equals space 2.18 space cross times space 10 to the power of negative 11 end exponent space open parentheses 1 over 1 squared minus 1 over 5 squared close parentheses
space space space space space equals space 2.18 space cross times space 10 to the power of negative 11 end exponent space open parentheses 24 over 25 close parentheses
space space space space space equals space 2.09 space cross times space 10 to the power of negative 11 end exponent ergs
space space space space space equals space 2.09 space cross times space 10 to the power of negative 18 end exponent straight J space space space space space space space space space left parenthesis 1 space erg space equals space 10 to the power of negative 7 end exponent straight J right parenthesis
When electron returns to ground state (i.e. to n = 1), energy emitted equals space 2.09 space cross times space 10 to the power of negative 11 end exponent space ergs
    We know, 
    straight E equals space hv space equals space hc over straight lambda
    straight lambda space equals space hc over straight E
 
 Substituting the values in the above expression
straight lambda space equals fraction numerator left parenthesis 6.626 space cross times space 10 to the power of negative 27 end exponent space erg space sec right parenthesis space left parenthesis 3 cross times 10 to the power of 10 space cm space straight s to the power of negative 1 end exponent right parenthesis over denominator 2.09 space cross times space 10 to the power of negative 11 end exponent space ergs end fraction
space space space equals space 9.51 space cross times space 10 to the power of negative 6 end exponent space cm space equals space 951 space straight Å