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 *n*_{1} = 2 and n_{2} = 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