$A$ point source of light emits photons of energy $4.8 eV$ at the rate $10^5$ photons per second. These photons are incident on a photo-sensitive sphere of work function $2.8 eV$ and radius $9 mm$. The sphere is initially neutral and the emitted photoelectrons are instantly swept away. The time after which the photoelectric emission stops is (in $s$)

$A$ metal surface of work function $1.07 eV$ is irradiated with light of wavelength $332 nm$. The retarding potential required to stop the escape of photo-electrons is .............. $V$.

In an experiment of photoelectric effect,the stopping potential was measured to be $V_{1}$ and $V_{2}$ with incident light of wavelength $\lambda$ and $\frac{\lambda}{2}$ respectively. The relation between $V_{1}$ and $V_{2}$ is:

Assertion : When ultraviolet light is incident on a photocell,its stopping potential is $V_0$ and the maximum kinetic energy of the photoelectrons is $K_{max}$. When the ultraviolet light is replaced by $X-$ rays,both $V_0$ and $K_{max}$ increase.
Reason : Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.

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

$A$ photon of energy $3.4 \ eV$ is incident on a metal having work function $2 \ eV$. The maximum kinetic energy $(K.E.)$ of photo-electrons is equal to ........... $eV$. (in $eV$)