When light of frequencies ${\nu _1}$ and ${\nu _2}$ $({\nu _1} > {\nu _2})$ is incident on a metal surface,the ratio of the maximum kinetic energy of the emitted photoelectrons is $1:k$. What is the threshold frequency of the metal?

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1:$ $A$ metallic surface is irradiated by a monochromatic light of frequency $v > v_0$ (the threshold frequency). If the incident frequency is now doubled,the photocurrent and the maximum kinetic energy are also doubled.
Statement $2:$ The maximum kinetic energy of photoelectrons emitted from a surface is linearly dependent on the frequency of the incident light. The photocurrent depends only on the intensity of the incident light.

When radiation of wavelength $\lambda$ is incident on a metallic surface,the stopping potential of ejected photoelectrons is $4.8 \, V$. If the same surface is illuminated by radiation of double the previous wavelength,then the stopping potential becomes $1.6 \, V$. The threshold wavelength of the metal is $... \lambda$.

When a certain photosensitive surface is illuminated with monochromatic light of frequency $v$,the stopping potential for the photocurrent is $-V_0/2$. When the surface is illuminated by monochromatic light of frequency $v/2$,the stopping potential is $-V_0$. The threshold frequency for photoelectric emission is

The maximum velocity of the photoelectron emitted by the metal surface is $v$. The charge and mass of the photoelectron are denoted by $e$ and $m$ respectively. The stopping potential in volt is

The work function of a substance is $4.0 \,eV$. The longest wavelength of light that can cause photoelectron emission from this substance is approximately ......... $nm$.