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Chapter 11: Problem 5

What are six particle conservation laws? Briefly describe them.

Short Answer

Expert verified
Six particle conservation laws include: 1. Conservation of Charge: The total electric charge in a system remains constant during any interactions or reactions. 2. Conservation of Energy: The total energy of an isolated system remains constant over time, no matter the internal changes or processes. 3. Conservation of Momentum: The total linear momentum of an isolated system remains constant over time, provided no external forces are acting on the system. This includes both linear and angular momentum. 4. Conservation of Baryon Number: The total baryon number is conserved in all physical processes, meaning the number of baryons remains the same before and after a reaction or interaction. 5. Conservation of Lepton Number: The total lepton number is conserved in all physical processes, meaning the number of leptons remains the same before and after a reaction or interaction. 6. Conservation of Color Charge: In strong force interactions, the total color charge (a quantum number associated with quarks) remains constant throughout any interactions. This principle is related to the theory of quantum chromodynamics (QCD).

Step by step solution

01

1. Conservation of Charge

In any physical process, the total electric charge is conserved. If a system has a net charge initially, it will remain the same after any interactions or reactions.
02

2. Conservation of Energy

The total energy of an isolated system remains constant over time, regardless of changes or processes occurring within it. This is true for both particle interactions and large-scale systems.
03

3. Conservation of Momentum

The total linear momentum of an isolated system remains constant over time, provided that no external forces are acting on the system. This includes both the conservation of linear momentum (in which the total momentum is conserved) and the conservation of angular momentum (in which the total rotational momentum about an axis is conserved).
04

4. Conservation of Baryon Number

The total baryon number (the number of baryons, such as protons and neutrons, minus the number of their corresponding antiparticles) is conserved in all physical processes. In simple terms, the total number of baryons remains the same before and after a reaction or interaction.
05

5. Conservation of Lepton Number

Similar to the conservation of baryon number, the lepton number (the number of leptons, such as electrons, muons, and neutrinos, minus the number of their corresponding antiparticles) is conserved in all physical processes. This means that the total number of leptons remains the same before and after a reaction or interaction.
06

6. Conservation of Color Charge

In the strong force interaction (the force that binds quarks together within particles like protons and neutrons), the total color charge is conserved. This means that the net color charge of a system, which is a quantum number associated with quarks, remains constant throughout any interactions. The concept of color charge is more complex than electric charge and is related to the theory of quantum chromodynamics (QCD).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Conservation of Charge
Imagine rubbing a balloon on your hair, and it sticks to a wall. That's an example of electric charge in action. More formally, the Conservation of Charge states that the total electric charge in an isolated system remains constant. It鈥檚 not possible to create or destroy electric charge during chemical reactions or physical processes. In a closed system, charges may transfer between objects, but if you sum up all the charges before and after the process, they balance out. An example is the electrolysis of water, where the total charge remains zero on both sides of the reaction.
Conservation of Energy
As you pedal a bike uphill, your muscles convert chemical energy into mechanical energy. The Conservation of Energy principle tells us that energy in an isolated system can change forms鈥攍ike from chemical to mechanical鈥攂ut its total amount doesn鈥檛 change. For instance, in a pendulum, kinetic energy converts to potential energy and back again, but the total energy remains constant. This principle is a cornerstone of physics and implies that perpetual motion machines are not possible.
Conservation of Momentum
When you're ice skating and push off another skater, you both glide off in opposite directions. This exemplifies the Conservation of Momentum. The total momentum, defined as the mass times velocity of an object, is conserved in an isolated system. If no external forces act on the system, the sum of all individual momenta before and after an event will be the same. This conservation is evident in events such as collisions or explosions, where the total momentum is distributed amongst the involved entities but the overall system's momentum remains unchanged.
Conservation of Baryon Number
When you eat, your body uses the proteins, which are comprised of amino acids containing baryons, primarily in protons and neutrons. The Conservation of Baryon Number ensures the net number of baryons (like protons and neutrons) remains constant during any physical process. It's a strict rule indicating that if you start with a certain number of baryons, you will end with that same number, even if they change forms or combine, as in nuclear fusion processes occurring within stars.
Conservation of Lepton Number
You might have heard about neutrinos, the tiny particles that rarely interact with matter. They're a type of lepton, and like baryons, leptons are governed by a conservation law. The total number of leptons鈥攖he Conservation of Lepton Number鈥攔emains the same in a closed system. For example, when a neutron decays into a proton, an electron and an anti-neutrino are emitted to conserve both the charge and lepton number.
Conservation of Color Charge
Zooming into a world much smaller than atoms takes us to quarks and gluons, whose interactions are governed by the strong nuclear force. Here, the Conservation of Color Charge comes into play. It鈥檚 similar to the conservation of electric charge but applies to the strong force interactions that hold quarks together within particles like protons and neutrons. This law upholds that the color charge鈥攁 property of quarks related to how they experience the strong force鈥攊s conserved. When quarks interact, they rearrange their color charges, but the total color remains in balance. The theory handling these interactions is quantum chromodynamics (QCD), which is a complex but essential part of understanding subatomic particles.

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Most popular questions from this chapter

Plans for an accelerator that produces a secondary beam of K mesons to scatter from nuclei, for the purpose of studying the strong force, call for them to have a kinetic energy of \(500 \mathrm{MeV} .\) (a) What would the relativistic quantity \(\gamma=\frac{1}{\sqrt{1-v^{2} / c^{2}}}\) be for these particles? (b) How long would their average lifetime be in the laboratory? (c) How far could they travel in this time?

The Andromeda Galaxy is the closest large galaxy and is visible to the naked eye. Estimate its brightness relative to the Sun, assuming it has luminosity \(10^{12}\) times that of the Sun and lies 0.613 Mpc away.

The primary decay mode for the negative pion is \(\pi^{-} \rightarrow \mu^{-}+\bar{\nu}_{\mu} .\) (a) What is the energy release in \(\mathrm{MeV}\) in this decay? (b) Using conservation of momentum, how much energy does each of the decay products receive, given the \(\pi^{-}\) is at rest when it decays? You may assume the muon antineutrino is massless and has momentum \(p=E / c,\) just like a photon.

(a) A particle and its antiparticle are at rest relative to an observer and annihilate (completely destroying both masses), creating two \(\gamma\) rays of equal energy. What is the characteristic \(\gamma\) -ray energy you would look for if searching for evidence of proton-antiproton annihilation? (The fact that such radiation is rarely observed is evidence that there is very little antimatter in the universe.) (b) How does this compare with the 0.511 -MeV energy associated with electron-positron annihilation?

Based on the quark composition of a neutron, show that is charge is 0 .
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