Particle physics
Elementary particles are those particles whose internal structures are unknown. Leptons, quarks and mediator particles are considered as the elementary particles.
Particles and Antiparticles
A particle is said to be antiparticle of a particle if that has equal mass and magnitude of electric charge, but nature of charge is opposite. Some examples of particle-antiparticle pair:
Electron and positron
They having equal mass and equal magnitude of charge (i.e., \(1.6 \times 10^{-19}\) c). When an electron combines with positron, they disappear.
Proton and antiproton
Antiproton is the antiparticle of a proton.
Neutron and antineutron
Antineutron is the antiparticle of neutron, Neutron & antineutron have zero electric charge.
Neutrino and anti-neutrino
Pauli proposed, in 1931, that β-decay is always accompanied by another particle of almost zero rest mass and zero-charge, called neutrino. Antineutrino is the antiparticle of neutrino.
Matter and antimatter
Antielements (i.e., positron, antiproton, antineutron) are responsible to form antimatter.
Annihilation
When a particle interacts with its antiparticle, whose masses of both particle and antiparticle are completely converted into energy (photons), usually, a pair of γ-rays (sometimes x-rays). This process of conversion of matter into energy is called annihilation.
Fig.1 Electron positron annihilation.
Pair production
An x-ray or γ-ray, may interact with the matter while traveling nearer from the nucleus. When a photon of x-ray or γ-ray passes through the nuclear field, a electron-positron pair (+ve & -ve) appears in place of photon. This materialization process of energy is known as pair production.
fig: pair production.
Concept of spin
Rotation of an object along its axis is called spin. It is quite different than classical physics in the context of elementary particles.
Half Spin
In this spin, particle reverse their direction in 2Ï€ rotation (i.e. upside turns down) and after another 2Ï€ rotation, come to their original position. Or, such particles can recover their original position after an rotation. Fermions are half-spin particles.
Integer Spin
The particles having Integer spin, recover their original position after \(2\pi\) rotation. Bosons are Integer spin particles.
Classification of Elementary particles
Elementary particles
Fermions
Bosons
| Leptons | quarks | gauge Boson | Higgs Boson |
|---|---|---|---|
| Electron (e-) | Up (u) | Gluons | |
| Electron neutrino(Ve) | Down(d) | Photons | |
| muon (μ) | Charm(c) | W and z Bosons | |
| muon neutrino (Vu) | Strange(s) | Gravitons | |
| Tau (Ï„) | Top(t) | ||
| Tau neutrino (VÏ„) | Bottom(b) |
Fermions
The elementary particles with half-integer Spins are called fermions. Half integers can be the odd multiples of \(\frac{1}{2}\). \([i.e \frac{1}{2}, \frac{3}{2}, \frac{5}{2}]\). Leptons & quarks belongs to this family. This particles obey pauli exclusion principle.
Leptons
Lighter elementary particles are incorporated in this class. There are six leptons.
Some important information of leptons are tabulated below:
| particle | Symbol | charge | rest mass(mev) |
|---|---|---|---|
| Electron | \(e^{-}\) | -e | 0.51 |
| Muon | \(\mu^{-}\) | -e | 106 |
| Tau | \(\tau^{-}\) | -e | 1784 |
| e-neutrino | \(V_e\) | 0 | 0 |
| \(\mu\)-neutrino | \(V_\mu\) | 0 | 0 |
| \(\tau\)-neutrino | \(V_\tau\) | 0 | 0 |
Quarks
Quarks are elementary particles which are the fundamental constants of matter. They are fermions. They combine to form composite particles called hadrons. Short description of quarks are tabulated below.
| Types of quarks | Symbol | Charg. | Baryon NO. | Antiquarks |
|---|---|---|---|---|
| Up | u | \(\pm\frac{2}{3}e\) | \(\pm\frac{1}{3}\) | \(\overline{u}\) |
| Down | d | \(-\frac{1}{3}e\) | \(\pm\frac{1}{3}\) | \(\overline{d}\) |
| Charm | c | \(\pm\frac{1}{3}e\) | \(\pm\frac{1}{3}\) | \(\overline{c}\) |
| Strange | s | \(-\frac{1}{3}e\) | \(\pm\frac{1}{3}\) | \(\overline{s}\) |
| Top | t | \(\pm\frac{1}{3}e\) | \(\pm\frac{1}{3}\) | \(\overline{t}\) |
| Bottom | b | \(-\frac{1}{3}e\) | \(\pm\frac{1}{3}\) | \(\overline{b}\) |
Bosons
the elementary particles with zero or integral Spin(0,1,2...) are bosons. Gauge bosons and Higgs bosons are examples of bosons. They do not obey pauli exclusion principle.
Hadrons
Hadrons are strongly interacting heavy composite particles. They are composed of quarks. They are basically two types: mesons & baryons. Mesons contain one quark and an antiquark. Baryons contain three quarks. The hadrons are classified as below
| Mesons | Baryons | ||
|---|---|---|---|
| k | Mesons | Nucleons | Hyperons |
| π | Mesons | proton | Lambda |
| η | Mesons | Neutron | Sigma |
Mesons
mesons are made up of a quark and an antiquark. They possess mass intermediate between electron and proton.
Baryons
Baryons are composite particles including nucleons & hyperons. They have half-integer spins. They have equal or greater mass of that the mass of a proton. Every baryon has an antiparticle.
Nucleons
these are the lightest baryons. This group includes protons, neutrons & their antiparticles.
Hyperons
Hyperons have mass value intermediate between those of neutron and deuteron. Actually, hyperons contain strange quarks.
Quarks & Baryons
Each baryon is combination of three quarks and baryon number is + for each baryon.
proton: \(P = uud\)
Total Charge, \(Q = \frac{2}{3}e + \frac{2}{3}e - \frac{1}{3}e = +e\)
Also, Baryon number, \(B = \frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 1\)
Similarly, Antiproton Contains, \(\overline{P} = \overline{u}\overline{u}\overline{d}\)
Neutron: \((n = udd)\)
Total Charge, \(Q = \frac{2}{3}e - \frac{1}{3}e - \frac{1}{3}e = 0\)
Also, Baryon number, \(B = \frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 1\)
Similarly, Antineutron, \(\overline{n} = \overline{u} \overline{d} \overline{d}\).
Sigma: \((\Sigma^{+} = uus)\)
Total Charge, \(Q = \frac{2}{3} e + \frac{2}{3} e - \frac{1}{3} e = + e\)
Also, Baryon no.1, \(B = \frac{1}{3} + \frac{1}{3} + \frac{1}{3} = 1\)
Similarly, \(\Sigma^{0}=uds\) & \(\Sigma^{-}=dds\)
| Baryon | q-combination | Charge |
|---|---|---|
| P | uud | +e |
| n | udd | 0 |
| \(\Lambda^{0}\) | uds | 0 |
| \(\Sigma^{+}\) | uus | +e |
| \(\Sigma^{0}\) | uds | 0 |
| \(\Sigma^{-}\) | dds | -e |
Three Generations of Quarks and Leptons
| Type | first | second | third |
|---|---|---|---|
| quarks | |||
| up-type | up(u) | charm(c) | top(t) |
| down-type | down(d) | strange(s) | bottom(b) |
| leptons | |||
| Charged | electron(e) | muon(μ) | tau(τ) |
| neutral | electron neutrino(νe) | muon neutrino(νμ) | tau neutrino(ντ) |
Universe
the universe is all around us, in our vision and beyond our Vision. The size of universe is still unknown. Many constituents of universe are invisible and are called dark matter and dark energy.
The branch of Science, which deals with the study of the origin, evolution & nature of the universe, is Called Cosmology.
Big-Bang
Big bang theory is the most widely accepted and popular theory. It explains not only the origin of all known matters, the laws of physics and the large Scale Structure of the universe, it also accounts for the expansion of universes and broad range of other phenomena.
Red Shift
According to Doppler effect, there is apparent change in wavelength of waves emitted by source when it is in motion with respect of observer. The wave-length is increased if the source is moving away from observer and is decreased if source is moving towards observer.
If the star is moving towards the earth wavelength of light emitted by star will be decreases and it's colour shifted toward Violet and the visible spectrum formed by such process is called blue shift.
As, the Star in the Galaxy moves away from Earth wavelength of light emitted by star will increases and shifts towards red and such a visible spectrum toward red end is called red shift.
Let us consider a galaxy moving away from us with a velocity v'. Then,
red shift (z) = \(\frac{V}{C}\) ---- (i)
where 'c' is velocity of light in vacuum.
\(\frac{V}{C} = \frac{\Delta\lambda}{\lambda}\) [∵ \(\Delta\lambda = \lambda - \lambda_0\)]
\(\therefore \Delta\lambda = \frac{V\lambda}{C}\)
Hubble's Law
Red shift shows that galaxy are moving away from us. This gives rise to the theory a universe is expanding the velocity with which galaxy moves away from us is proportional to their distance from earth. This law is given by Hubble. Hence it is known as Hubble's law.
According to Hubble's law the speed with which galaxy moves away from us is directly proportional to its distance from earth.
If v be the speed with which a galaxy moves from us and r be the distance of the earth, then,
\(v = H_0 r\)
Where, \(H_0\) is Hubble's Constant. It's Value is \(2 \times 10^{-11} \, m/s\).
Significance of Hubble's Constant:
Age of Universe
Suppose 'r' be the size of Universe and 't' be the age of universe. If Galaxy of the Universe moves away from us with velocity 'v'. Then, By Hubble's law:
\(v = H_0 r\)
If universe is expanding to a size R in time t then, \(R = vt\) → (i)
$$ t=\frac{1}{H_{0}} $$
\(t = 14 \times 10^{9}\) years
Hence, reciprocal of Hubble's constant estimate the age of universe.
Size of universe
If the Size of Universe is R and Speed of Galaxy becomes speed of Light. Then, by Hubble's Law, \(v = H_0 R\)
R = 6000 Mega par secs (Mpc)
\(=6000 \times 10^{6}\) pc
\(=6000 \times 10^{6} \times 3.2\) Light year
\(1 Mpc = 10^{6} pc\)
\(1 pc = 3.2\) light year
Critical density
The density of universe which determine the expanding nature of universe is called critical density. It is denoted by \(\rho_c\).
Let us consider, the universe as a Spherical volume of radius R and mass M. If m be the mass of a Galaxy and v be its escape velocity from the universe then its gravitational p.e. should be equal to k.e.
i.e., \(\frac{GMm}{R} = \frac{1}{2}mv^{2} \Rightarrow 2GM = v^{2}R\)
According to Hubble's law, also, \(V = H_{0}R\) → (i) \(M = \frac{4}{3}\pi R^{3}\rho_c\) → (ii)
Using eqn(ii) in eqn(i)
\(2G\cdot\frac{4}{3}\pi R^{3}\rho_c=H_{0}^{2}\cdot R^{3}\)
\(\rho_c=\frac{3H_{0}^{2}}{8\pi G}\) This gives value of critical density, i.e. \(5.8 \times 10^{-27} kg/m^{3}\).
Dark matter
The average density of all the matter in the universe is about 27% of critical density but average density of visible matter is about 4% and most of matter of universe are invisible and doesn't emit any kind of radiation, the invisible matter in the universe which does not emit any kind of radiation is called dark matter.
The invisible form of energy which can be source of a repulsive force causing the expansion of the universe to accelerate is known as dark energy.
Black Hole
If a spherical non-rotating body with mass m has a radius r less than R, nothing, not even light can escape from the surface of the body, such body is called black hole.
Gravitational wave
GTR → General Theory of Relativity of Albert Einstein.
Some properties of gravitational waves are:
- invisible.
- Speed is equal to speed of light.
- Obey the inverse square law.
- These could exist in any frequency, however, very low frequency waves would be impossible to detect.