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Question
Suppose in an imaginary world the angular momentum is quantized to be even integral multiples of h/2π. What is the longest possible wavelength emitted by hydrogen atoms in visible range in such a world according to Bohr's model?
Solution
In the imaginary world, the angular momentum is quantized to be an even integral multiple of h/2 π.
Therefore, the quantum numbers that are allowed are n1 = 2 and n2 = 4
We have the longest possible wavelength for minimum energy.
Energy of the light emitted (E) is given by
`E = 13.6 (1/n_1^2 - 1/n_2^2)`
`E = 13.6 [ 1/(2)^2 - 1/(4)^2]`
`E = 13.6 (1/4 - 1/16)`
`E = (13.6xx12)/64 = 2.55 eV`
Equating the calculated energy with that of photon, we get
2.55 eV = `(hc)/lamda`
`lamda = (hc)/2.55 = 1242/2.55 nm`
= 487.05 nm= 487 nm
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