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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Answer:
Grand state, n=1, energy is given by,
E
1
=−2.18×10
−11
ergs
Now, energy of the n=S (5
th
orbit} is given by,
E
s
=
(S)
2
E
1
=
2S
−2.18×10
−11
ergs
=−0.0872×10
−11
ergs
Energy required to go to the 5
th
orbit
=E
S
−E
1
=−0.0872−(−2.18)×10
−11
ergs
=2.0928×10
−11
ergs
Now, 1erg=10
−7
J
⇒2.0928×10
−11
ergs=2.0928×10
−18
J
For wavelength,
λ
1
=R[
(1)
2
1
=
(S)
2
1
]
where, R=1.0973×10
5
cm
−1
⇒
λ
1
=1.0973×10
5
[1−
2S
1
]
⇒λ=9.49×10
−5
cm
or, ≃9.5×10
−7
m
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