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Question : 9
Total: 27
State Bohr's quantization condition of angular momentum. Calculate the shortest wavelength of the Bracket series and state to which part of the electromagnetic spectrum does it belong.
OR
Calculate the orbital period of the electron in the first excited state of hydrogen atom.
OR
Calculate the orbital period of the electron in the first excited state of hydrogen atom.
Solution:
Statement of Bohr's quantization condition
Calculation of shortest wavelength
Identification of part of electromagnetic spectrum
Electron revolves around the nucleus only in those orbits for which the angular momentum is some integral ofh ∕ 2 π h
Also give full credit if a student write mathematicallym v r =
= R (
−
)
For Brackett Series,
Shortest wavelength is for the transition of electrons fromn i = ∞ n f = 4
= R (
) =
λ =
m
= 1458.5 nm on substitution of value of R 1
OR
Statement of the formula forr n
Statement of the formula forv n
Obtaining formula forT n
Getting expression forT 2 ( n = 2 )
Radius,r n =
n 2
velocity,v n =
Timeperiod,T n =
=
For first excited state of hydrogen atomn = 2
T 2 =
On calculation we getT 2 ≈ 1.22 × 10 − 15 s
Calculation of shortest wavelength
Identification of part of electromagnetic spectrum
Electron revolves around the nucleus only in those orbits for which the angular momentum is some integral of
Also give full credit if a student write mathematically
For Brackett Series,
Shortest wavelength is for the transition of electrons from
OR
Statement of the formula for
Statement of the formula for
Obtaining formula for
Getting expression for
Radius,
velocity,
Timeperiod,
For first excited state of hydrogen atom
On calculation we get
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