In the hydrogen spectrum,if an electron transitions from the $6^{th}$ orbit to the $3^{rd}$ orbit through multiple steps,what is the total number of spectral lines in the $U.V.$ region?

Maximum number of spectral lines possible when an electron jumps from $5^{th}$ excited state to ground state in a sample containing only one Hydrogen atom will be

The wavenumber of the first line $(n_2=3)$ in the Balmer series of hydrogen is $\bar{\nu}_1 \ cm^{-1}$. What is the wavenumber (in $cm^{-1}$) of the second line $(n_2=4)$ in the Balmer series of $He^{+}$?

If $\lambda_0$ and $\lambda$ are respectively the threshold wavelength and wavelength of incident light,the velocity of photoelectrons ejected from the metal surface is

An excited hydrogen atom emits light in the ultraviolet region at a frequency of $2.47 \times 10^{15} \ Hz$. Calculate the energy of a single photon. (Given: $h = 6.63 \times 10^{-34} \ J \cdot s$)

The kinetic energy of electrons emitted, when radiation of frequency $1.0 \times 10^{15} \ Hz$ hits a metal, is $2 \times 10^{-19} \ J$. What is the threshold frequency of the metal (in $Hz$)?
$(h = 6.6 \times 10^{-34} \ Js)$