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Question
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 × 10–11 ergs.
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Solution
Energy (E) of the nth Bohr orbit of an atom is given by,
`"E"_"n" = (-(2.18xx10^(-18))"Z"^2)/"n"^2`
Where,
Z = atomic number of the atom
Ground state energy = – 2.18 × 10–11 ergs
= - 2.18 × 10–11 × 10–7 J
= - 2.18 × 10–18 J
Energy required to shift the electron from n = 1 to n = 5 is given as:
ΔE = E5 – E1
`= (-(2.18xx10^(-18))(1)^2)/(5)^2 - (-2.18 xx 10^(-18))`
`= (2.18xx10^(-18))[1 - 1/25]`
`= (2.18xx10^(-18))(24/25)`
`= 2.0928 xx 10^(-18)"J"`
Wavelength of emitted light = `"hc"/"E"`
`= ((6.626xx10^(-34))(3xx10^(8)))/(2.0928xx10^(-18))`
`= 9.498 xx 10^(-8) "m"`
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