Balmer Series — Prelims Questions

An electron in a hydrogen atom makes a transition from the $n=4$ state to the $n=2$ state. Calculate the wavelength of the emitted photon. (Given: Rydberg constant $R_H = 1.097 \times 10^7\,\text{m}^{-1}$)

Which of the following transitions in the hydrogen atom corresponds to the H-alpha line of the Balmer series?

The energy of the electron in the $n$-th orbit of the hydrogen atom is given by $E_n = -13.6/n^2\,\text{eV}$. What is the energy of the photon emitted when an electron transitions from $n=5$ to $n=2$?

Which of the following statements about the Balmer series is INCORRECT?

The ratio of the longest wavelength of the Balmer series to the shortest wavelength of the Balmer series is:

If the wavelength of the H-alpha line ($n=3 \to n=2$) in the Balmer series is $656.3\,\text{nm}$, what is the frequency of the emitted photon? (Given: speed of light $c = 3 \times 10^8\,\text{m/s}$)