In an electron transition from an infinite state to the ground state in an $H$ atom,find the emitted wavelength. (in $nm$)

The shortest wavelength of $H$ atom in the Lyman series is $\lambda_{1}$. The longest wavelength in the Balmer series of $He^{+}$ is:

Two series of spectral lines of atomic hydrogen which do not belong to the infrared spectral region are

An electronic transition in a hydrogen atom results in the formation of the $H_\alpha$ line of the hydrogen spectrum in the Lyman series. The energies associated with the electron in each of the orbits involved in the transition (in $kcal \ mol^{-1}$) are:

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: $m_{e} = 9 \times 10^{-31} \ kg$, $h = 6.63 \times 10^{-34} \ J \cdot s$, $c = 3 \times 10^8 \ m/s$, $1 \ eV = 1.6 \times 10^{-19} \ J$.

$A$ surface ejects electrons when hit by green light but not when hit by yellow light. Will electrons be ejected if the surface is hit by red light?