Match List-$I$ (Fundamental Experiment) with List-$II$ (its conclusion) and select the correct option from the choices given below the list.

List-$I$	List-$II$
$a$. Franck-Hertz Experiment	$i$. Particle nature of light
$b$. Photo-electric Experiment	$ii$. Discrete energy levels of atom
$c$. Davisson-Germer Experiment	$iii$. Wave nature of electron
	$iv$. Structure of atom

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?

For a body moving with relativistic speed,if the velocity is doubled,then

In the following arrangement $y = 1.0\ mm$,$d = 0.24\ mm$ and $D = 1.2\ m$. The work function of the material of the emitter is $2.2\ eV$. The stopping potential $V_0$ needed to stop the photocurrent will be .............. $V$.

Dual nature of light is exhibited by

Statement $(I)$ : By increasing the potential difference between cathode and anode continuously in a photoelectric experiment,the photocurrent always increases continuously.
Statement $(II)$ : If two photons $A$ and $B$ of energies $2.5 \ eV$ and $3.5 \ eV$ respectively fall on a metal surface of work function $2.0 \ eV$,then the ratio of maximum kinetic energies emitted between $A$ and $B$ is $3$.
Statement $(III)$ : The maximum energy needed by an electron to come out from metal surface is called the work function of the metal.
Which of the following is correct?