Two streams of photons,possessing energies equal to twice and ten times the work function of a metal,are incident on the metal surface successively. The ratio of the maximum velocities of the photoelectrons emitted in the two respective cases is $x:y$. The value of $x$ is ...... .

$(i)$ In the explanation of the photoelectric effect,we assume one photon of frequency $f$ collides with an electron and transfers its energy. This leads to the equation for the maximum kinetic energy $E_{max}$ of the emitted electron as $E_{max} = hf - \phi_0$ (where $\phi_0$ is the work function of the metal). If an electron absorbs $2$ photons (each of frequency $f$),what will be the maximum energy for the emitted electron?
$(ii)$ Why is this fact (two-photon absorption) not taken into consideration in our discussion of the stopping potential?

Ultraviolet light of wavelength $300 \ nm$ and intensity $1.0 \ W/m^2$ is incident on the surface of a photosensitive material. If $1\%$ of the incident photons produce photoelectrons,the number of photoelectrons emitted from an area of $1.0 \ cm^2$ of the surface is:

An electron in the hydrogen atom jumps from excited state $n$ to the ground state. The wavelength so emitted illuminates a photosensitive material having work function $2.75 \ eV$. If the stopping potential of the photoelectron is $10 \ V$,then the value of $n$ is

$A$ metal surface is illuminated by light of wavelength $400 \ nm$. The kinetic energy of the emitted photoelectrons is found to be $1.68 \ eV$. The work function of the metal is ......... $eV$. $(hc = 1240 \ eV \cdot nm)$

For a metal with a work function of $6.6 \text{eV}$, which of the following wavelengths of incident radiation does not cause the photoelectric effect (in $\text{nm}$)? (Take Planck's constant $h = 6.6 \times 10^{-34} \text{J s}$ and speed of light $c = 3 \times 10^8 \text{m/s}$)