Photoelectric emission takes place from a certain metal at threshold frequency $\nu$. If the radiation of frequency $2\nu$ is incident on the metal plate, the maximum velocity of the emitted photoelectron will be ($m = \text{mass of electron}$, $h = \text{Planck's constant}$)

Light of wavelength '$\lambda$' which is less than threshold wavelength is incident on a photosensitive material. If incident wavelength is decreased so that emitted photoelectrons are moving with some velocity, then the stopping potential:

The beam of light has three wavelengths $4144 \,\mathring A$,$4972 \,\mathring A$,and $6216 \,\mathring A$ with a total intensity of $3.6 \times 10^{-5} \, W/m^2$ equally distributed amongst the three wavelengths. The beam falls normally on an area of $1 \, cm^2$ of a clean metallic surface with a work function of $2.3 \, eV$. Assume that there is no loss of light by reflection and that each energetically capable photon ejects one electron. Calculate the number of photoelectrons liberated in $2 \, s$.

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

Five elements $A, B, C, D$ and $E$ have work functions $1.2 \, eV, 2.4 \, eV, 3.6 \, eV, 4.8 \, eV$ and $6 \, eV$ respectively. If light of wavelength $4000 \, Å$ is allowed to fall on these elements, then photoelectrons are emitted by:

The slope of the graph between the frequency of incident light and the stopping potential for a given surface is: