The variation of photo-current with collector potential for different frequencies of incident radiation $v_{1}, v_{2}$ and $v_{3}$ is as shown in the graph. Then:

Statement $1$: $A$ metal surface is irradiated by monochromatic light of frequency $v > v_0$. The maximum kinetic energy and stopping potential are $K_{max}$ and $V_0$ respectively. If the frequency of the incident light is doubled, then $K_{max}$ and $V_0$ will also be doubled. Statement $2$: The stopping potential and maximum kinetic energy of photoelectrons emitted from a surface depend linearly on the frequency of the incident light.

When a metal is irradiated by monochromatic light,the maximum kinetic energy of the photoelectrons is $1.2 \ eV.$ If the frequency of the light is increased by $50 \%$,then the maximum kinetic energy of the photoelectrons is $3.6 \ eV.$ Evaluate the work function of the metal.

Light of wavelength $\lambda_{\text{ph}}$ falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is $\phi$ and the anode is a wire mesh of conducting material kept at a distance $d$ from the cathode. $A$ potential difference $V$ is maintained between the electrodes. If the minimum de Broglie wavelength of the electrons passing through the anode is $\lambda_e$,which of the following statement$(s)$ is(are) true?

The metallic surface is illuminated with monochromatic light of wavelength $\lambda$ and the stopping potential for the photoelectric current is $5V_0$. When the same metallic surface is illuminated with light of wavelength $2\lambda$,the stopping potential is $V_0$. What is the threshold wavelength for the surface?

When green light is incident on the surface of a metal, it emits photo-electrons, but there is no such emission with yellow light. Which one of the following colours can produce emission of photo-electrons?