Nick Connor

What is Baryon

Baryon is any fermion that undergo strong interactions. In general, particles that do participate in strong interactions are called hadrons: protons and neutrons are hadrons. The hadrons are further sub-divided into baryons and mesons, according to the number of quarks they contain. Protons and neutrons each contain three quarks; they belong to the family of particles called the baryons. Other baryons are the lambda, sigma, xi, and omega particles. On the other hand mesons bosons and they are composed of two quarks: a quark and an antiquark. Besides charge and spin (1/2 for the baryons), two other quantum numbers are assigned to these particles: baryon number (B) and strangeness (S). Baryons have a baryon number, B, of 1, while their antiparticles, called antibaryons, have a baryon number of −1. A nucleus of deuterium (deuteron), for example, contains one proton and one neutron (each with a baryon number of 1) and has a baryon number of 2.

Since baryons make up most of the mass of ordinary atoms, the everyday matter is often referred to as baryonic matter.

The conservation of baryon number is an important rule for interactions and decays of baryons. No known interactions violate conservation of baryon number.

Baryon Number

In particle physics, the baryon number is used to denote which particles are baryons and which particles are not. Each baryon has a baryon number of 1 and each antibaryon has a baryon number of -1. Other non-baryonic particles have a baryon number of 0. Since there are exotic hadrons like pentaquarks and tetraquarks, there is a general definition of baryon number as:

where n_q is the number of quarks, and n_q is the number of antiquarks.

The baryon number is a conserved quantum number in all particle reactions. The term conserved means that the sum of the baryon number of all incoming particles is the same as the sum of the baryon numbers of all particles resulting from the reaction. A slight asymmetry in the laws of physics allowed baryons to be created in the Big Bang.

Law of Conservation of Baryon Number

In analyzing nuclear reactions, we apply the many conservation laws. Nuclear reactions are subject to classical conservation laws for, momentum, angular momentum, and energy (including rest energies).  Additional conservation laws, not anticipated by classical physics, are electric charge, lepton number and baryon number. Certain of these laws are obeyed under all circumstances, others are not.

Baryon number is a generalization of nucleon number, which is conserved in nonrelativistic nuclear reactions and decays. The law of conservation of baryon number states that:

The sum of the baryon number of all incoming particles is the same as the sum of the baryon numbers of all particles resulting from the reaction.

For example, the following reaction has never been observed:

even if the incoming proton has sufficient energy and charge, energy, and so on, are conserved. This reaction does not conserve baryon number since the left side has B =+2, and the right has B =+1.

On the other hand, the following reaction (proton-antiproton pair production) does conserve B and does occur if the incoming proton has sufficient energy (the threshold energy = 5.6 GeV):

As indicated, B = +2 on both sides of this equation.

From these and other reactions, the conservation of baryon number has been established as a basic principle of physics.

This principle provides basis for the stability of the proton. Since the proton is the lightest particle among all baryons, the hypothetical products of its decay would have to be non-baryons. Thus, the decay would violate the conservation of baryon number. It must be added some theories have suggested that protons are in fact unstable with very long half-life (~10³⁰ years) and that they decay into leptons. There is currently no experimental evidence that proton decay occurs.

See also:

Laws of Conservation

Lepton Number

In particle physics, the lepton number is used to denote which particles are leptons and which particles are not. Each lepton has a lepton number of 1 and each antilepton has a lepton number of -1. Other non-leptonic particles have a lepton number of 0. The lepton number is a conserved quantum number in all particle reactions. A slight asymmetry in the laws of physics allowed leptons to be created in the Big Bang.

The conservation of lepton number means that whenever a lepton of a certain generation is created or destroyed in a reaction, a corresponding antilepton from the same generation must be created or destroyed. It must be added, there is a separate requirement for each of the three generations of leptons, the electron, muon and tau and their associated neutrinos.

Example: Electron Capture

Consider the electron capture mode. The reaction involves only first generation leptons: electrons and neutrinos:

The antineutrino cannot be emitted, because in this case the conservation law would not be fulfilled. The particle emitted with the neutron must be a neutrino.

Example: Neutron Decay

Consider the decay of the neutron. The reaction involves only first generation leptons: electrons and neutrinos:

Since the lepton number must be equal to zero on both sides and it was found that the reaction is a three-particle decay (the electrons emitted in beta decay have a continuous rather than a discrete spectrum),  the third particle must be an electron antineutrino.

Example: Muon Decay

The observation of the following decay reaction leads to the conclusion that there is a separate lepton number for muons which must also be conserved.

This is in fact the most common decay mode of the ^–.

See also:

Leptons

What is Lepton

A lepton is an elementary, half-integer spin (spin  1⁄2) particle that does not undergo strong interactions. Particles that do participate in strong interactions are called hadrons.

There are six leptons in the present structure, the electron, muon, and tau particles and their associated neutrinos. Leptons are said to be elementary particles; that is, they do not appear to be made up of smaller units of matter. They behave as point-like particles. All leptons are fermions, i.e. leptons are spin- 1⁄2 particles and thus that they are subject to the Pauli exclusion principle. This fact has key implications for the building up of the periodic table of elements.

Any of the six elementary particles that (with their antiparticles) are not quarks are leptons. Two main classes of leptons exist:

• Charged leptons. Charged leptons can combine with other particles to form various composite particles such as atoms and positronium.
  • Electron. The electron is a negatively charged particle with a mass that is approximately 1/1836 that of the proton. Electrons are located in an electron cloud, which is the area surrounding the nucleus of the atom. The electron is only one member of a class of elementary particles, which forms an atom.
  • Muon. The muon is an elementary particle similar to the electron, with an electric charge of −1 e and a spin of ½. Muons are heavier, having more than 200 times as much mass as electrons. The muon is an unstable subatomic particle with a mean lifetime of 2.2 µs.
  • Tau. The tau (τ), also called the tau lepton, tau particle, or tauon, is an elementary particle similar to the electron, with an electric charge of −1 e and a spin of ½. Taus are approximately 3,700 times more massive than electrons. Tau leptons have a lifetime of 2.9×10⁻¹³ s.
• Neutral leptons (better known as neutrinos) are electrically neutral particles that rarely interact with anything, and are consequently rarely observed. A neutrino is an elementary subatomic particle with infinitesimal mass (less than 0.3 eV..?) and with no electric charge. Neutrinos are weakly interacting subatomic particles with ½ unit of spin.
  • Electron neutrino. The electron neutrino is a subatomic lepton elementary particle which has the symbol ν_e. It has no net electric charge and a spin of ½. Together with the electron it forms the first generation of leptons, hence the name electron neutrino.
  • Muon neutrino. The muon neutrino is a subatomic lepton elementary particle which has the symbol  ν_μ. It has no net electric charge and a spin of ½. Together with the muon it forms the second generation of leptons, hence the name muon neutrino.
  • Tau neutrino. The tau neutrino is a subatomic lepton elementary particle which has the symbol  ν_τ. It has no net electric charge and a spin of ½. Together with the tauon it forms the third generation of leptons, hence the name tau neutrino.

Law of Conservation of Lepton Number

In particle physics, the lepton number is used to denote which particles are leptons and which particles are not. Each lepton has a lepton number of 1 and each antilepton has a lepton number of -1. Other non-leptonic particles have a lepton number of 0. The lepton number is a conserved quantum number in all particle reactions. A slight asymmetry in the laws of physics allowed leptons to be created in the Big Bang.

The conservation of lepton number means that whenever a lepton of a certain generation is created or destroyed in a reaction, a corresponding antilepton from the same generation must be created or destroyed. It must be added, there is a separate requirement for each of the three generations of leptons, the electron, muon and tau and their associated neutrinos.

Example: Electron Capture

Consider the electron capture mode. The reaction involves only first generation leptons: electrons and neutrinos:

The antineutrino cannot be emitted, because in this case the conservation law would not be fulfilled. The particle emitted with the neutron must be a neutrino.

Example: Neutron Decay

Consider the decay of the neutron. The reaction involves only first generation leptons: electrons and neutrinos:

Since the lepton number must be equal to zero on both sides and it was found that the reaction is a three-particle decay (the electrons emitted in beta decay have a continuous rather than a discrete spectrum),  the third particle must be an electron antineutrino.

Example: Muon Decay

The observation of the following decay reaction leads to the conclusion that there is a separate lepton number for muons which must also be conserved.

This is in fact the most common decay mode of the ^–.

See also:

Fundamental Particles

What is Lepton

A lepton is an elementary, half-integer spin (spin  1⁄2) particle that does not undergo strong interactions. Particles that do participate in strong interactions are called hadrons.

There are six leptons in the present structure, the electron, muon, and tau particles and their associated neutrinos. Leptons are said to be elementary particles; that is, they do not appear to be made up of smaller units of matter. They behave as point-like particles. All leptons are fermions, i.e. leptons are spin- 1⁄2 particles and thus that they are subject to the Pauli exclusion principle. This fact has key implications for the building up of the periodic table of elements.

Any of the six elementary particles that (with their antiparticles) are not quarks are leptons. Two main classes of leptons exist:

• Charged leptons. Charged leptons can combine with other particles to form various composite particles such as atoms and positronium.
  • Electron. The electron is a negatively charged particle with a mass that is approximately 1/1836 that of the proton. Electrons are located in an electron cloud, which is the area surrounding the nucleus of the atom. The electron is only one member of a class of elementary particles, which forms an atom.
  • Muon. The muon is an elementary particle similar to the electron, with an electric charge of −1 e and a spin of ½. Muons are heavier, having more than 200 times as much mass as electrons. The muon is an unstable subatomic particle with a mean lifetime of 2.2 µs.
  • Tau. The tau (τ), also called the tau lepton, tau particle, or tauon, is an elementary particle similar to the electron, with an electric charge of −1 e and a spin of ½. Taus are approximately 3,700 times more massive than electrons. Tau leptons have a lifetime of 2.9×10⁻¹³ s.
• Neutral leptons (better known as neutrinos) are electrically neutral particles that rarely interact with anything, and are consequently rarely observed. A neutrino is an elementary subatomic particle with infinitesimal mass (less than 0.3 eV..?) and with no electric charge. Neutrinos are weakly interacting subatomic particles with ½ unit of spin.
  • Electron neutrino. The electron neutrino is a subatomic lepton elementary particle which has the symbol ν_e. It has no net electric charge and a spin of ½. Together with the electron it forms the first generation of leptons, hence the name electron neutrino.
  • Muon neutrino. The muon neutrino is a subatomic lepton elementary particle which has the symbol  ν_μ. It has no net electric charge and a spin of ½. Together with the muon it forms the second generation of leptons, hence the name muon neutrino.
  • Tau neutrino. The tau neutrino is a subatomic lepton elementary particle which has the symbol  ν_τ. It has no net electric charge and a spin of ½. Together with the tauon it forms the third generation of leptons, hence the name tau neutrino.

Law of Conservation of Lepton Number

In particle physics, the lepton number is used to denote which particles are leptons and which particles are not. Each lepton has a lepton number of 1 and each antilepton has a lepton number of -1. Other non-leptonic particles have a lepton number of 0. The lepton number is a conserved quantum number in all particle reactions. A slight asymmetry in the laws of physics allowed leptons to be created in the Big Bang.

The conservation of lepton number means that whenever a lepton of a certain generation is created or destroyed in a reaction, a corresponding antilepton from the same generation must be created or destroyed. It must be added, there is a separate requirement for each of the three generations of leptons, the electron, muon and tau and their associated neutrinos.

Conservation of Lepton Number – Electron Capture

Consider the electron capture mode. The reaction involves only first generation leptons: electrons and neutrinos:

The antineutrino cannot be emitted, because in this case the conservation law would not be fulfilled. The particle emitted with the neutron must be a neutrino.

Conservation of Lepton Number – Neutron Decay

Consider the decay of the neutron. The reaction involves only first generation leptons: electrons and neutrinos:

Since the lepton number must be equal to zero on both sides and it was found that the reaction is a three-particle decay (the electrons emitted in beta decay have a continuous rather than a discrete spectrum),  the third particle must be an electron antineutrino.

Conservation of Lepton Number – Muon Decay

The observation of the following decay reaction leads to the conclusion that there is a separate lepton number for muons which must also be conserved.

This is in fact the most common decay mode of the ^–.

See also:

Laws of Conservation

Law of Conservation of Electric Charge

In physics, there are two very important principles concerning the electric charge.

First is the law of conservation of electric charge. This law states that:

The algebraic sum of all the electric charges in any closed system is constant.

The only way to change the net charge of a system is to bring in charge from elsewhere, or remove charge from the system.

Charge can be created and destroyed, but only in positive-negative pairs.

Conservation of charge is thought to be a universal conservation law. No experimental evidence for any violation of this principle has ever been observed. In particle physics, charge conservation means that in elementary particle reactions that create charged particles, equal numbers of positive and negative particles are always created, keeping the net amount of charge unchanged. Even in high-energy interactions in which particles are created and destroyed, such as the creation of positron-electron pairs, the total charge of any closed system is exactly constant.

The second important principle is:

The magnitude of charge of the electron or proton is a natural unit of charge.

We say that charge is quantized. That is, every observable amount of electric charge is always an integer multiple of this basic unit. This unit is called the elementary charge, e, approximately equal to 1.602×10⁻¹⁹ coulombs (except for particles called quarks, which have charges that are integer multiples of  ¹⁄₃e).

Conservation of Charge in Nuclear Reactions

Important examples of the law of conservation of electric charge occur in nuclear reactions such as the radioactive decay of nuclei and the nuclear fission.  In these reactions a nucleus transforms into a different type of nucleus or nuclei.

Consider a typical fission reaction such as the one listed below.

Typically, when uranium 235 nucleus undergoes fission, the nucleus splits into two smaller nuclei (triple fission can also rarely occur), along with a few neutrons (the average is 2.43 neutrons per fission by thermal neutron) and release of energy in the form of heat and gamma rays. From these reactions we find that in the fission the parent nucleus:

• ²³⁵U contains 92 protons (a charge of +92e),
• incident neutron is electrically neutral.

The fission fragments:

• ¹³⁹Ba contains 56 protons (a charge of +56e),
• ⁹⁴Ba contains 36 protons (a charge of +36e)

We see that the total charge is 92e before and after the reaction; thus, charge is conserved. It is noteworthy, the total number of nucleons before and after a reaction are also the same.

Conservation of Charge in Positron-Electron Pair Production

The law of conservation of electric charge can be demonstrated also on positron-electron pair production. Since a gamma ray is electrically neutral and sum of the electric charges of electron and positron is also zero, the electric charge in this reaction is also conserved.

Ɣ → e^– + e⁺

It must be added, in order for electron-positron pair production to occur, the electromagnetic energy of the photon must be above a threshold energy, which is equivalent to the rest mass of two electrons. The threshold energy (the total rest mass of produced particles) for electron-positron pair production is equal to 1.02MeV (2 x 0.511MeV) because the rest mass of a single electron is equivalent to 0.511MeV of energy. If the original photon’s energy is greater than 1.02MeV, any energy above 1.02MeV is according to the conservation law split between the kinetic energy of motion of the two particles. The presence of an electric field of a heavy atom such as lead or uranium is essential in order to satisfy conservation of momentum and energy. In order to satisfy both conservation of momentum and energy, the atomic nucleus must receive some momentum. Therefore a photon pair production in free space cannot occur.

Conservation of Electric Charge in Neutrino Discovery

In 1931, Pauli proposed that another particle must be emitted in the beta decay process, because the electrons emitted in beta decay have a continuous rather than a discrete spectrum appeared to contradict conservation of energy, under the then-current assumption that beta decay is the simple emission of an electron from a nucleus. This another particle was later named by Fermi the neutrino. It was clear, this particle must be highly penetrating and that the conservation of electric charge requires the neutrino to be electrically neutral. This would explain why it was so hard to detect this particle. The term neutrino comes from Italian meaning “little neutral one” and neutrinos are denoted by the Greek letter ν (nu). In the process of beta decay the neutrino carries the missing energy and also in this process the law of conservation of energy remains valid.

See also:

Laws of Conservation

Example: Neutron Star Rotation

A neutron star is the collapsed core of a large star (usually of a red giant). Neutron stars are the smallest and densest stars known to exist, but they are rotating extremely rapidly. This rapid rotation is a direct consequence of the law of conservation of angular momentum. As the star’s core collapses, its rotation rate must increase, because of conservation of angular momentum, hence newly formed neutron stars must rotate at up to several hundred times per second. Some neutron stars emit beams of electromagnetic radiation that make them detectable as pulsars.

For example:

Assume a neutron star of a radius of 7 x 10⁵ km, which collapses under its own gravitation to a radius of 10 km. This star is rotating at a frequency of 1.0 revolution every 30 days. Assume that the star is a homogenous sphere at all times, and loses no mass.

From the law of conservation of angular momentum:

I₁ω₁ = I₂ω₂

where the subscripts 1 and 2 refer to initial star and neutron star, respectively. The moment of inertia of a sphere about its central axis is:

I = ⅖ m₁r₁²

therefore

See also:

Angular Momentum

Whar is Angular Momentum

In physics, the linear momentum, p = mv, has a rotational analog. It is called angular momentum  (rarely, moment of momentum or rotational momentum), L, and for an object rotating about a fixed axis with angular velocity ω, it is defined as:

L = Iω

It is an important quantity in physics because it is a conserved quantity:

The angular momentum of an isolated system remains constant in both magnitude and direction.

When there is zero net torque acting on an object, and the object is rotating about a fixed axis or about an axis through its center of mass whose direction doesn’t change, we can write:

I₁ω₁ = I₂ω₂ = constant

Like conservation of energy and of linear momentum, this principle is a universal conservation law, valid at all scales from atomic and nuclear systems to the motions of galaxies. The angular momentum is a vector quantity and therefore it can be generalized as:

The vector sum of the angular momenta of the parts of an isolated system is constant.

This puts a strong constraint on the types of rotational motions which can occur in an isolated system. If one part of the system is given an angular momentum in a given direction, then some other part or parts of the system must simultaneously be given exactly the same angular momentum in the opposite direction.

The law of conservation of angular momentum explains the angular acceleration of an ice skater as she brings her arms and legs closer to the vertical axis of rotation. By bringing part of the mass of her body closer to the axis she decreases her body’s moment of inertia. Because angular momentum is the product of moment of inertia (I) and angular velocity (ω), and the angular momentum remains constant according to this law, the angular velocity of the skater must increase.

I₁ω₁ = I₂ω₂

See also:

Angular Momentum

Law of Conservation of Angular Momentum

In physics, the linear momentum, p = mv, has a rotational analog. It is called angular momentum  (rarely, moment of momentum or rotational momentum), L, and for an object rotating about a fixed axis with angular velocity ω, it is defined as:

L = Iω

It is an important quantity in physics because it is a conserved quantity:

The angular momentum of an isolated system remains constant in both magnitude and direction.

When there is zero net torque acting on an object, and the object is rotating about a fixed axis or about an axis through its center of mass whose direction doesn’t change, we can write:

I₁ω₁ = I₂ω₂ = constant

Like conservation of energy and of linear momentum, this principle is a universal conservation law, valid at all scales from atomic and nuclear systems to the motions of galaxies. The angular momentum is a vector quantity and therefore it can be generalized as:

The vector sum of the angular momenta of the parts of an isolated system is constant.

This puts a strong constraint on the types of rotational motions which can occur in an isolated system. If one part of the system is given an angular momentum in a given direction, then some other part or parts of the system must simultaneously be given exactly the same angular momentum in the opposite direction.

The law of conservation of angular momentum explains the angular acceleration of an ice skater as she brings her arms and legs closer to the vertical axis of rotation. By bringing part of the mass of her body closer to the axis she decreases her body’s moment of inertia. Because angular momentum is the product of moment of inertia (I) and angular velocity (ω), and the angular momentum remains constant according to this law, the angular velocity of the skater must increase.

I₁ω₁ = I₂ω₂

Example: Neutron Star Rotation

A neutron star is the collapsed core of a large star (usually of a red giant). Neutron stars are the smallest and densest stars known to exist, but they are rotating extremely rapidly. This rapid rotation is a direct consequence of the law of conservation of angular momentum. As the star’s core collapses, its rotation rate must increase, because of conservation of angular momentum, hence newly formed neutron stars must rotate at up to several hundred times per second. Some neutron stars emit beams of electromagnetic radiation that make them detectable as pulsars.

For example:

Assume a neutron star of a radius of 7 x 10⁵ km, which collapses under its own gravitation to a radius of 10 km. This star is rotating at a frequency of 1.0 revolution every 30 days. Assume that the star is a homogenous sphere at all times, and loses no mass.

From the law of conservation of angular momentum:

I₁ω₁ = I₂ω₂

where the subscripts 1 and 2 refer to initial star and neutron star, respectively. The moment of inertia of a sphere about its central axis is:

I = ⅖ m₁r₁²

therefore

Conservation of Angular Momentum in Fluid Mechanics

Euler’s turbomachine equation, or sometimes called Euler’s pump equation, plays a central role in turbomachinery as it connects the specific work Y and the geometry and velocities in the impeller. The equation is based on the concepts of conservation of angular momentum and conservation of energy.

The Euler’s turbomachine equations are:

Shaft torque:                         T_shaft    =                                     ρQ(r₂V_t2 – r₁V_t1)

Water horsepower:             P_w         =     ω . T_shaft        =      ρQ(u₂V_t2 – u₁V_t1)

Pump head:                            H           =     P_w / ρgQ      =      (u₂V_t2 – u₁V_t1)/g

where

• r₁ and r₂ are the diameters of the impeller at the inlet and outlet respectively.
• u₁ and u₂ are the absolute velocities of the impeller (u₁ = r₁ . ω) at the inlet and outlet respectively.
• V_t1 and V_t2 are the tangential velocities of the flow at the inlet and outlet respectively.

Euler’s turbomachine equations can be used to predict the impact of changing the impeller geometry on the head. It does not matter when we deal with a pump or with a turbine. If torque and angular velocity are of like sign, work is being done on the fluid (a pump or compressor). If torque and angular velocity are of opposite sign work is being extracted from the fluid (a turbine). Thus for the design aspect of turbines and pumps, the Euler equations are extremely useful.

See also:

Laws of Conservation

Momentum of Photon

A photon, the quantum of electromagnetic radiation,  is an elementary particle, which is the force carrier of the electromagnetic force. The modern photon concept was developed (1905) by Albert Einstein to explain of the photoelectric effect, in which he proposed the existence of discrete energy packets during the transmission of light.

In 1916, Einstein extended his concept of light quanta (photons) by proposing that a quantum of light has linear momentum. Although a photon is massless, it has momentum, which is related to its energy E, frequency f, and wavelength by:

Thus, when a photon interacts with another object, energy and momentum are transferred, as if there were a collision between the photon and matter in the classical sense.

Momentum of a Photon – Compton Scattering

The Compton formula was published in 1923 in the Physical Review. Compton explained that the X-ray shift is caused by particle-like momentum of photons. Compton scattering formula is the mathematical relationship between the shift in wavelength and the scattering angle of the X-rays. In the case of Compton scattering the photon of frequency f collides with an electron at rest. Upon collision, the photon bounces off electron, giving up some of its initial energy (given by Planck’s formula E=hf), While the electron gains momentum (mass x velocity), the photon cannot lower its velocity. As a result of momentum conservation law, the photon must lower its momentum given by:

So the decrease in photon’s momentum must be translated into decrease in frequency (increase in wavelength Δλ = λ’ – λ). The shift of the wavelength increased with scattering angle according to the Compton formula:

where λ is the initial wavelength of photon λ’ is the wavelength after scattering, h is the Planck constant = 6.626 x 10^-34 J.s, m_e is the electron rest mass (0.511 MeV)c is the speed of light Θ is the scattering angle. The minimum change in wavelength (λ′ − λ) for the photon occurs when Θ = 0° (cos(Θ)=1) and is at least zero. The maximum change in wavelength (λ′ − λ) for the photon occurs when Θ = 180° (cos(Θ)=-1). In this case the photon transfers to the electron as much momentum as possible. The maximum change in wavelength can be derived from Compton formula:

The quantity h/m_ec is known as the Compton wavelength of the electron and is equal to 2.43×10⁻¹² m.

See also:

Photon

What is the Law of Conservation of Momentum

In general, the law of conservation of momentum or principle of momentum conservation states that the momentum of an isolated system is a constant. The vector sum of the momenta (momentum is equal to the mass of an object multiplied by its velocity) of all the objects of a system cannot be changed by interactions within the system. In classical mechanics, this law is implied by Newton’s laws. This principle is a direct consequence of Newton’s third law.

Let us assume the one dimensional elastic collision of two billiard balls,, the ball A and the ball B. We assume the net external force on this system of two balls is zero—that is, the only significant forces during the collision are the forces that each ball exerts on the other. According to Newton’s third law, the two forces are always equal in magnitude and opposite in direction. Hence, the impulses that act on the two balls are equal and opposite, and the changes in momentum of the two balls are equal and opposite.

These two balls are moving with velocities v_A and v_B along the x axis before the collision. After the collision, their velocities are v’_A and v’_B. The conservation of the total momentum demands that the total momentum before the collision is the same as the total momentum after the collision.

The law of conservation of linear momentum in words:

If no net external force acts on a system of particles, the total linear momentum of the system cannot change.

See also:

Laws of Conservation