Question

Which of the following reactions obey the conservation of baryon number? (a) \(p + p \rightarrow p + e^+\); (b) \(p + n \rightarrow 2e^+ + e^-\); (c) \(p \rightarrow n + e^- + \overline{\nu}_e\); (d) \(p + \overline{p} \rightarrow 2\gamma\).

Short answer

Reactions (c) and (d) conserve baryon number.

Step-by-step solution

Define Baryon Number Conservation

In particle physics, the baryon number is a conserved quantity. The baryon number of a baryon (such as a proton or neutron) is +1, and for an anti-baryon (such as an anti-proton), it is -1. Non-baryons, like electrons and photons, have a baryon number of 0. To check conservation, ensure the sum of baryon numbers on both sides of the equation is equal.

Analyze Reaction (a)

Reaction (a): \(p + p \rightarrow p + e^+\). The left side contains two protons, each with a baryon number of 1, so the total is 2. The right side has one proton (baryon number of 1) and one positron (baryon number of 0), giving a total of 1. Left side total (2) does not equal right side total (1). This reaction does not conserve baryon number.

Analyze Reaction (b)

Reaction (b): \(p + n \rightarrow 2e^+ + e^-\). The left side has a proton (baryon number 1) and a neutron (baryon number 1), making a total of 2. The right side consists of positrons and an electron, all with baryon number 0, adding to 0. The left side total (2) is not equal to the right side total (0). This reaction does not conserve baryon number.

Analyze Reaction (c)

Reaction (c): \(p \rightarrow n + e^- + \overline{u}_e\). The proton on the left has a baryon number of 1. On the right, the neutron has a baryon number of 1, while the electron and the electron anti-neutrino each have a baryon number of 0. Left side total (1) equals right side total (1). This reaction conserves baryon number.

Analyze Reaction (d)

Reaction (d): \(p + \overline{p} \rightarrow 2\gamma\). The left side includes a proton with baryon number 1 and an anti-proton with baryon number -1. These add up to 0. On the right, the photons have a baryon number of 0. Left side total (0) equals right side total (0). This reaction conserves baryon number.

Key concepts

Particle Physics

Particle physics is a branch of physics that explores the smallest building blocks of matter and how they interact. It delves into the realm of subatomic particles, which include elementary particles such as quarks, leptons, and gauge bosons. These elements combine to form more complex particles like protons and neutrons.

In particle physics, interactions are described by fundamental forces, which are conveyed by particles like the photon for electromagnetic force and gluons for strong force. Understanding these interactions helps scientists unravel the mysteries of the universe, such as why mater dominates over antimatter and how the universe began.

Key discoveries in particle physics have been groundbreaking, such as the identification of the Higgs boson and the development of the Standard Model, which serves as a comprehensive theory for explaining electromagnetic, weak, and strong nuclear interactions. Through experiments in particle accelerators, like the Large Hadron Collider, scientists continue to expand our knowledge of the cosmos.

Baryons and Anti-Baryons

Baryons are subatomic particles made up of three quarks, examples include protons and neutrons. These particles are essential components of atomic nuclei and are classified based on their quark composition and properties. In contrast, anti-baryons consist of three antiquarks, and exhibit properties opposite to their baryon counterparts, such as the anti-proton, which is the antimatter equivalent of the proton.

The classification of baryons and anti-baryons is crucial in particle physics because it allows scientists to understand matter-antimatter interactions, which are fundamental to explaining why the universe consists mostly of matter. Baryons carry a baryon number of +1, while anti-baryons carry a baryon number of -1. This is pivotal in conservation laws, particularly the conservation of baryon number.

Conservation Laws

Conservation laws are fundamental principles in physics that assert certain quantities remain constant throughout physical processes. In particle physics, one of the key conservation laws is the conservation of baryon number. This law states that the total baryon number before and after a reaction must remain the same.

Conservation laws help ensure that reactions in particle and nuclear physics are predictable and consistent. For instance:

• Baryon number: Baryons have a number of +1, anti-baryons -1, and non-baryons, like electrons, have 0.
• Charge conservation: The total charge is conserved in all reactions.
• Energy and momentum conservation: Total energy and momentum remain constant in isolated systems.

By applying these laws, scientists can verify whether hypothetical reactions occur naturally and conform to the rules of physics, aiding in our understanding of the laws governing the universe and the consistency observed in nature.