In a photocell,bichromatic light of wavelengths $2475 \ \mathring{A}$ and $6000 \ \mathring{A}$ is incident on a cathode whose work function is $4.8 \ eV$. If a uniform magnetic field of $3 \times 10^{-5} \ T$ exists parallel to the plate,the radius of the path described by the photoelectron will be ............ $cm$ (mass of electron $= 9 \times 10^{-31} \ kg$).

$A$ monochromatic light is incident on a metallic plate having work function $\phi$. An electron,emitted normally to the plate from a point $A$ with maximum kinetic energy,enters a constant magnetic field,perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point $B$. The distance between $A$ and $B$ is (Given: The magnitude of charge of an electron is $e$ and mass is $m$,$h$ is Planck's constant,and $c$ is velocity of light. Take the magnetic field exists throughout the path of electron).

If $m$ is the mass of an electron and $c$ is the speed of light,then the ratio of the wavelength of a photon of energy $E$ to the wavelength of an electron of the same energy is:

Assertion $(A)$: In the photoelectric effect,on increasing the intensity of light,both the number of electrons emitted and the kinetic energy of each of them increase,but the photoelectric current remains unchanged.
Reason $(R)$: The photoelectric current depends only on the wavelength of light.

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?

Given below are two statements:
Statement $I$: Out of microwaves,infrared rays,and ultraviolet rays,ultraviolet rays are the most effective for the emission of electrons from a metallic surface.
Statement $II$: Above the threshold frequency,the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light.
In the light of the above statements,choose the correct answer from the options given below: