An electromagnetic wave of wavelength $\lambda$ is incident on a photosensitive surface of negligible work function. If the photoelectrons emitted from this surface have the de-Broglie wavelength $\lambda_{1}$,then:

An electron moving with speed $v$ and a photon moving with speed $c$ have the same de Broglie wavelength. The ratio of the kinetic energy of the electron to that of the photon is -

Photoelectric effect experiments are performed using three different metal plates $p, q$ and $r$ having work functions $\phi_p=2.0 \ eV, \phi_q=2.5 \ eV$ and $\phi_r=3.0 \ eV$,respectively. $A$ light beam containing wavelengths of $550 \ nm, 450 \ nm$ and $350 \ nm$ with equal intensities illuminates each of the plates. The correct $I-V$ graph for the experiment is:

The dual nature of radiation is demonstrated by:

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?

Match List-$I$ with List-$II$:

List-$I$	List-$II$
$A$. $E = hv$	$I$. de Broglie wavelength
$B$. Diffraction and Interference	$II$. Particle nature of light
$C$. $\lambda = h/p$	$III$. Wave nature of light
$D$. Compton effect	$IV$. Energy of photon

Choose the correct answer from the options given below: