a)

Millikan’s oil-drop experiment

https://www.youtube.com/watch?v=X9LAmsALnxo

Two up quarks and one down quark are found in each proton. One up quark and two down quarks are found in neutrons.

u = + \frac{2}{3}e and d = - \frac{1}{3}

Quarks are carrying fractional charges inside protons and neutrons. This is because nuclear power rises enormously if it is pulled apart. As a result, fractional charges can occur in nature; observable charges are still an integral multiple of the electrical charge.

b)

Step 1: Recall the electric and magnetic field basic relations

After being accelerated by 1 volt of electricity, an electron gains energy.

eV = \frac{1}{2} mv^2 .................(1)

When electron passes through magnetic field region

Force acting on electron F = evB

Centripetal force F = \frac{mv^2}{r}

evB = \frac{mv^2}{r} ...............................(2)

Where, B - magnetic field, v - velocity, e - electron charge, m - mass, r - radius and V - potential

Step 2: Set up an equation for velocity

From equation (1)

v^2 = \frac{2eV}{m}

v = \sqrt{2V \frac{e}{m}}

From equation (2)

eB = \frac{mv}{r}

v = Br \frac{e}{m}

It can be concluded from these relations that the dynamics of an electron is calculated not by e and m separately, but

by the ratio e/m.

c)

Atom 1: Atom 2:

Because of collisions and recombination with other gas molecules, ions of gases have no chance of meeting their respective electrons **at atmospheric pressure.** As a consequence, at atmospheric pressure, gases serve as insulators. Electrons have a chance of touching their respective electrodes and creating a current **at low pressures**. As a result, at these pressures, they conduct electricity.

d)

The minimum energy needed for a conduction electron to leave the metal surface is known as the work function of the metal. The energy levels of all electrons in an atom are different. When a photon-emitting ray strikes a metal surface, electrons emerge from various levels at various energies. As a result, the energy distributions of the emitted electrons vary.

e)

Within the additive constant, a particle's absolute energy value is arbitrary. Therefore, while the wavelength ( \lambda ) associated with an electron is significant, the frequency ( \upsilon ) associated with an electron has no direct physical significance. As a result, the product \upsilon \lambda (phase speed) has no physical meaning.

The speed of a group is expressed as follows

v_G = \frac{dv}{dK}

v_G = \frac{dv}{d \frac{1}{\lambda}}

v_G = \frac{dE}{dp}

v_G = \frac{\frac{p^2}{2m}}{dp}

v_G = \frac{p}{m}

This quantity has a physical meaning