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

The photoelectric effect occurs only when the incident light has more than a certain minimum:

When electromagnetic radiation of wavelength $310 \ nm$ falls on the surface of a metal having work function $3.55 \ eV$, the velocity of photoelectrons emitted is $x \times 10^5 \ ms^{-1}$. The value of $x$ is (Nearest integer). Given: $m_{e} = 9 \times 10^{-31} \ kg$, $h = 6.63 \times 10^{-34} \ J \cdot s$, $c = 3 \times 10^8 \ m/s$, $1 \ eV = 1.6 \times 10^{-19} \ J$.

Find the frequency of light that corresponds to photons of energy $5.0 \times 10^{-5} \ erg$.

Which energy level transition among the following will have the least wavelength?

Which will be the first emission line in the infrared region of the hydrogen atomic spectrum?