Properties of Longitudinal Progressive Waves

Longitudinal wave motion refers to wave motion in which particles of medium vibrate along the direction of propagation of wave.

Properties:

1. All the particles have same Amplitude, Frequency and Time Period

2. There is a gradual Phase difference between successive particles

3. All the particles vibrating in Phase will be at a distance equal to nƛ. Here n=1,2,3etc. It means the   minimum distance between two particles vibrating in Phase is equal to wave length.

4. When the particle moves in same distance as that of wave, it is in a region of compression.

5. When the particle moves in opposite direction as that of wave it is in a region of Refraction.

6. When the particle is at mean position, it is a region of maximum Compression or Refraction.

7. When the particle is at extreme position, the medium around particles has its normal density, with compression on one side and rare fraction on other side.

Ionic Conductivity - Detailed Explanation

Thermal Radiation - Important points

The process of heat transfer from a body by virtue of its temperature with out involvement of intervening medium is called Radiation. The radiant energy is transported by electromagnetic waves because these waves can travel through vacuum.

The Radiation emitted by a body by virtue of its temperature is called Thermal Radiation. It is an inherent property of all bodies.

According to Prevost theory of heat exchanger, every body emits and absorbs radiant energy continuously as long as its temperature is above 0 K.

At low temperature, the emission rate is small while at higher temperatures it increases rapidly as 4th power of absolute temperature. 

At ordinary and moderate high temperature, mostly longer waves(infrared) are emitted but at very high temperatures shorter waves are also emitted.

Properties of Thermal Radiation:

i)  It travels through empty space with the velocity of light.

ii) It undergoes Reflection, Refraction and total internal reflection obeying the same law as light.

iii) It exhibits the phenomenon of interference, diffraction and polarisation.

iv) It exerts a small, but finite pressure on the surface on which it is incident. This is called as pressure of thermal radiation.

v)  It obeys inverse square law

Some important terms related to Thermal Radiation are  Spectral Energy Density, Total Energy Density, Emmisive Power & absorptive power

Spectral Energy Density

Spectral Energy Density for a particular wavelength is the energy per unit volume per unit range of wavelength.

Total Energy Density

Total energy density of thermal radiation at any point is the total radiant energy per unit volume around that point due to all wavelengths.

Emmissive Power

The emissive power of a body at a given temperature and for a given wavelength, is defined as the ratio radiant energy absorbed for a second by unit surface area of the body per unit wavelength range.

Absorptive power

The absorptive power of a body at a given temperature and for a given wavelength is defined as the ratio of radiant energy absorbed per second by unit surface area of the body to the total energy falling per second on the same area. 

Black body and its Radiation

What is a Black body?

Energy distribution in black body radiation

Laws of Black body Radiation

Kirchoff's Law

Stefan's-Boltzmann law

Wien's Law

Rayleigh-Jeans Law

Planck's Law

MILLER INDICES

Paulis Hypothesis of Beta Decay

Pauli introduced concept of third particle, a neutral particle which gets emitted in β⁻decay. This particle has the generic name of Neutrino.

The total energy is shared by 3 particles

The recoil nucleus
The Electron
The Neutrino

Because of its comparatively great mass, the recoil energy of Nucleus is very small and nearly all Kinetic Energy is shared between the Beta particle and the Neutrino.

In addition to laws of conservation of charge and energy, we must also apply the laws of conservation Linear and angular momentum to every nuclear process. Taking our reference system as the parent nucleus at rest, the vector sum of Linear Momenta of the recoil nucleus, the beta particle and neutrino must be zero.

To conserve angular momentum in β⁻decay, we note that parent and daughter nuclei are isobars; i.e. they have equal number of nucleons. Hence, the total change in nuclear angular momenta will be either zero or an integral multiple of ℏ.

The beta particle has an intrinsic spin angular momenta of 1/2ℏ.The vector sum of angular momenta of Neutrino and beta particle will be either zero or one in units of ℏ.

The present accepted theory, which is supported by experimental evidence shows that there are two types of neutrino or two components of Neutrino. It has been found that the axis of spin of neutrino is parallel to its direction of motion; one type spins according to the left hand rule with respect to its direction of motion as its axis, the other component spins according to right hand rule.

The first type is usually called neutrino represented by symbol 𝜈, the second type is called antineutrino.
 
The spin vector of neutrino points opposite to direction of its motion.

The spin vector of anti neutrino points in the direction of its motion.

Another way of saying this is that the helicity of neutrino is negative and that of anti neutrino is positive or one has right handed helicity and other has left handed helicity.
 

Nature of Orbits for a body projected from earth with different speeds

Minimum velocity required for an object to orbit around the Earth  is  Vs =√gR = 8KmSec⁻¹

Let Ve be the escape velocity  required for a body to escape Earth's gravitational field.

Let if  'V' be velocity with which a body is projected from Earth.

Then,

1. V < Vs → body falls to ground
2. V=Vs → body rotates round the Earth in circular orbit closer to surface of Earth.
3. Vs < V < Ve → body revolves in elliptical orbit
4. V=Ve → body just escapes from Gravitational Field
5. V>Ve → body moves in interstellar space with velocity equal to √❲V²-Ve²❳
6. V<Ve → Total Energy of body is Negative 
7. V=Ve → Total Energy of body is Zero.