Class 12th

1.4 

(a) Electric charge of a body is quantized, this means that only integers (1,2,3, ….n) number of electrons can be transferred from one body to the other. Charges are not transferred in fraction. Hence, a body possesses total charge only in integers.

(b) In macroscopic i.e. large scale charges, the charges used are huge as compared to the electric charge of electrons or protons. Therefore, it is ignored and it is considered that electric charge is continuous.

1.3 The units of the given equation 

$\frac{{ke}^2}{G{m}_e{m}_p}$ is

e = Electric charge in C

k = $\frac{1}{4\pi {?}_0}$ in N $m^2{C}^{-2},$ where ${?}_0$ = Permittivity of free space = 8.854 $*{10}^{-12}$ $C^2{N}^{-1}$ $m^{-2}$

G = Gravitational constant = N $$

$m^2{kg}^{-2}$

${\mathrm{m}}_{\mathrm{e}}=\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{n}\mathrm{}\mathrm{i}\mathrm{n}\mathrm{}\mathrm{k}\mathrm{g},\mathrm{}\mathrm{}{\mathrm{m}}_{\mathrm{p}}=\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{}\mathrm{i}\mathrm{n}\mathrm{}\mathrm{k}\mathrm{g}$

Therefore

$\frac{{ke}^2}{G{m}_e{m}_p}$ = $\frac{\left[\mathrm{N}{m}^2{C}^{-2}\right]*\left[C^2\right]}{\left[\mathrm{N}{m}^2{kg}^{-2}\right]\left[kg\right]\left[kg\right]}$= $M^0{L}^0{T}^0$

So the given equation is dimensionless

We have the following values

e = 1.6 $*{10}^{-19}$ C

G = 6.67  $*{10}^{-11}$${\mathrm{Nm}}^2{kg}^{-2}$ kg

${\mathrm{m}}_{\mathrm{e}}=9.1*{10}^{-31}$ kg

${\mathrm{m}}_{\mathrm{p}}=1.66*{10}^{-27}$

The numerical value of this ratio is given by

$\frac{{ke}^2}{G{m}_e{m}_p}$ = $\frac{\left[\mathrm{N}{m}^2{C}^{-2}\right]*\left[C^2\right]}{\left[\mathrm{N}{m}^2{kg}^{-2}\right]\left[kg\right]\left[kg\right]}$ = $\frac{1}{4\pi {?}_0}$ = $*\frac{e^2}{G{m}_e{m}_p}$= 
$\frac{1}{4*\pi *8.854\mathrm{}*{10}^{-12}}$ $*\frac{{(1.6\mathrm{}*{10}^{-19})}^2}{6.67*{10}^{-11}*{9.1*{10}^{-31}*1.66*{10}^{-27}}_{}}$

 = 2.284$*{10}^{39}$

The Davisson-Germer experiment was conducted to test the De-broglie hypothesis and know wave nature of electrons. In this experiment, a beam of electrons was emitted from an electron gun with known acceleration to strike a nickel crystal placed inside a vacuum chamber.

After striking the surface, electrons are scattered from the crystal surface at different angles. The diffraction pattern obtained through this experiment was similar to that produced by X-rays, which is wave.

The Davisson-Germer experiment provided the first experimental proof of the wave nature of matter and de Broglie's hypothesis right.

Electromagnetic waves do not require a medium to propagate because they generate self-sustaining oscillations of magnetic and electric fields. Hence, it can travel through the vacuum of space. A changing magnetic field generates an electric field and vice versa. This property allows the wave to carry energy across space. The phenomenon is applicable to sunlight and other forms of EM radiation that travel through space to reach Earth. They cover millions of kilometers while reaching Earth. The EM wave theory is fundamental to understanding phenomena like cosmic observations, satellite communication, and solar radiation.

The entire range of electromagnetic radiation, arranged to increase and decrease the wavelength is called the electromagnetic (EM) spectrum. In the following order, it includes - radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. All these regions have unique properties and applications. For example, X-rays used in medical imaging,  visible light in everyday vision, infrared in remote controls and thermal imaging and radio waves are used in communication. This is an important concept that helps in classifying and utilizing different EM waves.

Significance of de Broglie's Hypothesis in Modern Physics (NCERT-based answer):

De Broglie's hypothesis is a revolutionary idea which changed the understanding of matter and wave as we know it. This hypothesis introduced the concept that particles of matter, like electrons, and Proton, can behave like wave and have wave-like properties, just as light exhibits both wave and particle nature.

According to de Broglie, any moving particle has a wavelength given by:

$\lambda = \frac {h} {p} = \frac {h} {mv}$

where $\lambda$ is the wavelength, $h$ is Planck's constant, $m$ is the mass, and $v$ is the velocity of the particle.

The photoelectric effect when light is projected in a metal surface, it's surface ejects electron (which are in outermost shell or free electron). This happens because the light provides additional energy to the electron to detach itself from metal surface. Well to do this light must have a certain amount of energy which in other words can be said the right frequency of light is required for photoelectric effect. 

This frequency must be above a certain minimum value (called threshold frequency) fixed for every metal, regardless of its intensity. Photoelectric effect cannot be explained by the wave theory of light.

The net magnetic flux through any closed surface is zero, according to Gauss's Law for magnetism.
Mathematically,
? B · dA = 0.
It states that all magnetic field lines that enter a surface must exit from it as well. In this way, it is different from the electric charges which can exist independently as positive and negative.

The Earth's magnetic field makes a magnetic inclination or dip with the horizontal plane at a particular location. It shows how much the magnetic field is tilted from the horizontal. It gets tilted due to the Earth's magnetic nature. The formula is:
tan I = B_V / B_H,
where B_V is the vertical component and B_H is the horizontal component of the Earth's magnetic field.