Light of wavelength $2475 \, Å$ is incident on barium. Photoelectrons emitted describe a circle of radius $100 \, cm$ in a magnetic field of flux density $\frac{1}{\sqrt{17}} \times 10^{-5} \, T$. The work function of the barium is .............. $eV$ (Given $\frac{e}{m} = 1.7 \times 10^{11} \, C/kg$)

Consider the following statements $A$ and $B$ and identify the correct choice in the given answers.
$A$. Tightly bound electrons of target material scatter $X$-ray photon,resulting in the Compton effect.
$B$. Photoelectric effect takes place with free electrons.

Which of the following effects support the quantum nature of $EM$ radiation? $(1)$ Photoelectric effect $(2)$ Compton effect $(3)$ Doppler effect $(4)$ Field effect

When a monochromatic point source of light is placed at $0.1\, m$ from a photocell,the cut-off voltage and saturation current are $0.8\, V$ and $24\, mA$ respectively. If the same source is placed at $0.2\, m$ away from the photocell,then the cut-off voltage and saturation current will be:

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?

Two electrons are moving with the same speed $v$. One electron enters a region of a uniform electric field,while the other enters a region of a uniform magnetic field. If the de-Broglie wavelengths of the two electrons after some time are ${\lambda _1}$ and ${\lambda _2}$ respectively,then: