$A$ hydrogen atom in the ground state is given an energy of $10.2 \ eV$. How many spectral lines will be emitted due to the transition of electrons?

Hydrogen atoms are excited from ground state to the state of principal quantum number $4$. Then,the number of spectral lines observed will be . . . . . . .

If the series limit frequency of the Balmer series is $\nu_{B}$,then the series limit frequency of the Brackett series is

The shortest wavelength in the Lyman series is $912 \ \text{Å}$. Then, the longest wavelength in the series must be (in $\text{Å}$)

For a hydrogen atom,$\lambda_1$ and $\lambda_2$ are the wavelengths corresponding to the transitions $1$ and $2$ respectively,as shown in the figure. The ratio of $\lambda_1$ and $\lambda_2$ is $\frac{x}{32}$. The value of $x$ is:

What is the wavelength of light for the least energetic photon emitted in the Lyman series of the hydrogen spectrum (in $\text{ nm}$)? (Take $hc = 1240 \text{ eV nm}$)