An electron of mass $m$ and a photon have the same energy $E$. The ratio of the wavelength of the electron to that of the photon is: ($c$ being the velocity of light)

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:

The spectrum obtained from an electric lamp or a red-hot heater is:

Find the number of photons emitted per second from a source of light which results in a photocurrent with drift velocity of $1.5 \ m/s$ in a conductor with cross-section area $0.25 \ m^2$ and volume density of electrons $10^{20} \ m^{-3}$. (Assume that $60\%$ of photons emitted result in electron emission).

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 the following columns:

Column-$I$	Column-$II$
$A$. Hallwachs $\&$ Lenard	$P$. Transformers
$B$. Franck-Hertz	$Q$. Microwave
$C$. Klystron valve	$R$. Quantization of energy levels
$D$. Nicola Tesla	$S$. Photoelectric effect