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