The distance between the $3^{rd}$ and $2^{nd}$ Bohr's orbits in the hydrogen atom is

$A$ photon of wavelength $3000 \ \mathring{A}$ strikes a metal surface. The work function of the metal is $2.13 \ eV$. What is the kinetic energy of the emitted photoelectron (in $eV$)? $\left(h=6.626 \times 10^{-34} \ J \ s\right)$

The energy of an electron in an orbit of a hydrogen-like ion with an orbit radius of $52.9 \ pm$ in $J$ is (ground state energy of an electron in a hydrogen atom is $-2.18 \times 10^{-18} \ J$).

The ionization energy of a hydrogen atom is $13.6 \ eV$. The energy required to excite the electron in a hydrogen atom from the ground state $(n=1)$ to the first excited state $(n=2)$ is (Note: The question asks for energy per atom in Joules. Given $1 \ eV = 1.602 \times 10^{-19} \ J$)

Which one of the following transitions of an electron in a hydrogen atom emits radiation of the lowest wavelength?

The value of Planck's constant is $6.63 \times 10^{-34} \ J \ s$. The speed of light is $3 \times 10^{17} \ nm \ s^{-1}$. Which value is closest to the wavelength in nanometers of a quantum of light with a frequency of $6 \times 10^{18} \ s^{-1}$?