$A$ 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 $eV$)

$A$ photon and an electron have equal energy $E$. The ratio $\lambda_{\text{photon}} / \lambda_{\text{electron}}$ is proportional to:

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 .............. $V$.

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?

Which of the following support the quantum nature of the $EM$ radiations?
$(A)$ Photoelectric effect
$(B)$ Compton effect
$(C)$ Doppler effect
$(D)$ Field effect

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?