Question

Suppose, in certain conditions only those transitions are allowed to hydrogen atoms in which the principal quantum number $n$ changes by $2$.
(a) Find the smallest wavelength emitted by hydrogen.
(b) List the wavelengths emitted by hydrogen in the visible range $\left(380nmto780nm\right)$

Answer 1

$\left(a\right)n_1=1,n_2=3$

$E=13.6(\frac{1}{1}-\frac{1}{9})=13.6\times \frac{8}{9}=\frac{hc}{\lambda }$

or $\frac{13.6\times 8}{9}=\frac{4.14\times {10}^{-15}\times 3\times {10}^8}{\lambda }$

$\Rightarrow \lambda =\frac{4.14\times {10}^{-7}\times 3}{13.6\times 8}=103$nm

$\left(b\right)$ As $n$ changes by $2$, we may consider $n=2$ to $n=4$

then $E=13.6(\frac{1}{4}-\frac{1}{16})=13.6\times \frac{16-4}{64}=2.55$eV

and $2.55=\frac{1242}{\lambda }$ or $\lambda =\frac{1242}{2.55}=487$nm