Question

Suppose in an imaginary world the angular momentum is quantized to be even intergral multiples of $\frac{h}{2\pi }$. What is the longest possible wavelength emitted by hydrogen atoms in visible range in such a world according to Bohr's model ?

Answer 1

Even quantum numbers are allowed

$n_1=2,n_2=4$

For minimum energy or for longest possible wavelength.

E = $13.6(\frac{1}{n_2^2}-\frac{1}{n_2^2})$

= $13.6[\frac{1}{(2{)}^2}-\frac{1}{(4{)}^2}]$

= $13.6(\frac{1}{14}-\frac{1}{16})$

= $\frac{13.6\times 12}{64}=2.55$

i.e $2.55=\frac{hc}{\lambda }$

$\lambda =\frac{hc}{2.55}=\frac{1242}{2.55}nm$

= 487.05 nm = 487 nm