Which of the following statements regarding the energy of the stationary state is true in the following one-electron system?

The work function of a metal is $4.2 \, eV$. If radiation of $2000 \, \mathring{A}$ falls on the metal,then the kinetic energy of the fastest photoelectron is:

The ratio between kinetic energy and the total energy of the electrons of a hydrogen atom according to Bohr's model is

If an electron is moving in the $n^{th}$ orbit around the nucleus with a velocity $v$ and radius $r$,then the value of $n$ is .........

The wavelength of the second line of the Balmer series of a hydrogen atom is $\lambda \ nm$. What is the wavelength of the first line of the Lyman series of the $He^{+}$ ion (in $nm$)?

Threshold frequency,$v_0$ is the minimum frequency which a photon must possess to eject an electron from a metal. It is different for different metals. When a photon of frequency $1.0 \times 10^{15} \ s^{-1}$ was allowed to hit a metal surface,an electron having $1.988 \times 10^{-19} \ J$ of kinetic energy was emitted. Calculate the threshold frequency of this metal. Show that an electron will not be emitted if a photon with a wavelength equal to $600 \ nm$ hits the metal surface.