Light is incident on a metallic plate having a work function of $ 110 \times 10^{-20} \ J $. If the produced photoelectrons have zero kinetic energy, then the angular frequency of the incident light is . . . . . . $ rad/s $. $( h = 6.63 \times 10^{-34} \ J \cdot s )$

The wavelength of light in the visible region is about $390\; nm$ for violet colour,about $550\; nm$ (average wavelength) for yellow-green colour and about $760\; nm$ for red colour.
$(a)$ What are the energies of photons in $(eV)$ at the $(i)$ violet end,$(ii)$ average wavelength (yellow-green colour),and $(iii)$ red end of the visible spectrum? (Take $h=6.63 \times 10^{-34} \;J s$ and $1 \;eV = 1.6 \times 10^{-19} \;J$)
$(b)$ From which of the photosensitive materials with work functions listed in the table,and using the results of $(i), (ii)$ and $(iii)$ of $(a)$,can you build a photoelectric device that operates with visible light?

Metal	Work function $\phi_{0} (eV)$	Metal	Work function $\phi_{0} (eV)$
$Cs$	$2.14$	$Al$	$4.28$
$K$	$2.30$	$Hg$	$4.49$
$Na$	$2.75$	$Cu$	$4.65$
$Ca$	$3.20$	$Ag$	$4.70$
$Mo$	$4.17$	$N$	$5.15$
$Pb$	$4.25$	$Pt$	$5.65$

In an experiment on the photoelectric effect,the frequency $\nu$ of the incident light is plotted against the stopping potential $V_0$. The work function of the photoelectric surface is given by ($e$ is the electronic charge):

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$ : The photoelectric effect does not take place,if the energy of the incident radiation is less than the work function of a metal.
Reason $R$ : Kinetic energy of the photoelectrons is zero,if the energy of the incident radiation is equal to the work function of a metal.
In the light of the above statements,choose the most appropriate answer from the options given below.

The ratio of work functions of two metals $A$ and $B$ is $1:2$. If radiations of frequencies $f$ and $2f$ are incident on the surfaces of $A$ and $B$ respectively,the ratio of the maximum kinetic energies of the emitted photoelectrons will be: (Given $f >$ threshold frequency of $A$ and $2f >$ threshold frequency of $B$)

When a photon of energy $8 \ eV$ is incident on a metal surface with a threshold frequency of $1.6 \times 10^{15} \ Hz$,the maximum kinetic energy of the emitted photoelectrons is .......... $eV$. (Given: $h = 6.6 \times 10^{-34} \ Js, 1 \ eV = 1.6 \times 10^{-19} \ J$)