The work function of a substance is $3.0 \ eV$. The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately: (in $nm$)

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 light of frequency $8 \times 10^{14} \ Hz$ is incident on a surface,photoelectrons are emitted with a maximum speed of $7 \times 10^5 \ m/s$. The threshold frequency for this surface is ..........

The work functions of cesium $(Cs)$ and lithium $(Li)$ metals are $1.9 \ eV$ and $2.5 \ eV$,respectively. If we incident light of wavelength $550 \ nm$ on these two metal surfaces,then the photoelectric effect is possible for which case?

Two photons of energies twice and thrice the work function of a metal are incident on the metal surface. Then,the ratio of maximum velocities of the photoelectrons emitted in the two cases respectively,is

$A$ photoelectric surface is illuminated successively by monochromatic light of wavelength $\lambda$ and $\frac{\lambda}{2}$. If the maximum kinetic energy of the emitted photoelectrons in the first case is one-third that in the second case,the work function of the surface of the material is ($c=$ speed of light,$h=$ Planck's constant).