An electron makes a transition from the orbit $n=3$ to the orbit $n=1$ in a hydrogen atom. What is t

Question

An electron makes a transition from the orbit $n=3$ to the orbit $n=1$ in a hydrogen atom. What is the wavelength of the emitted radiation in terms of the Rydberg constant $R$?

Professor PC Thomas Classes · Answer

(a) : For a transition from $n_2=3$ to $n_1=1$, the wave number is given by the Rydberg formula: $\frac{1}{\lambda} = R \left[ \frac{1}{n_1^2} - \frac{1}{n_2^2} \right] = R \left[ \frac{1}{1^2} - \frac{1}{3^2} \right] = R \left[ 1 - \frac{1}{9} \right] = R \left[ \frac{8}{9} \right] = \frac{8R}{9}$. Inverting this expression to solve for the wavelength yields $\lambda = \frac{9}{8R}$.