Light of wavelength $2475 \, Å$ is incident on barium. Photoelectrons emitted describe a circle of radius $100 \, cm$ in a magnetic field of flux density $\frac{1}{\sqrt{17}} \times 10^{-5} \, T$. The work function of the barium is .............. $eV$ (Given $\frac{e}{m} = 1.7 \times 10^{11} \, C/kg$)

Answer the following questions:
$(a)$ Quarks inside protons and neutrons are thought to carry fractional charges $[(+2/3)e, (-1/3)e]$. Why do they not show up in Millikan's oil-drop experiment?
$(b)$ What is so special about the combination $e/m$? Why do we not simply talk of $e$ and $m$ separately?
$(c)$ Why should gases be insulators at ordinary pressures and start conducting at very low pressures?
$(d)$ Every metal has a definite work function. Why do all photoelectrons not come out with the same energy if incident radiation is monochromatic? Why is there an energy distribution of photoelectrons?
$(e)$ The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations:
$E = h\nu, p = \frac{h}{\lambda}$
But while the value of $\lambda$ is physically significant,the value of $\nu$ (and therefore,the value of the phase speed $\nu\lambda$) has no physical significance. Why?

When a light source of power $P$ emitting monochromatic light of wavelength $\lambda$ is kept at a distance $r$ from a photosensitive surface of work function $\phi$ and surface area $A$,which of the following is the wrong option?

$A$ radiation of $3.8 eV$ falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of $2 \times 10^{-4} T$. If the radius of the largest circular path followed by these electrons is $30 mm$,then the work function of the metal is (Mass of electron $m_{e} = 9 \times 10^{-31} kg$) (in $eV$)

Match the following table.

$List-I$	$List-II$
$A$. Michelson-Morley experiment	$I$. The existence of anti-matter
$B$. Stern-Gerlach experiment	$II$. The existence of de-Broglie matter waves
$C$. Davisson-Germer experiment	$III$. Electrons have spins
$D$. Anderson discovery of positron	$IV$. The non-existence of ether

Consider the following statements: $(1)$ Both wave and particle nature are required for a complete understanding of light. $(2)$ Light cannot exhibit both wave and particle nature simultaneously in a single experiment.