Question

State what quantities are conserved when balancing a nuclear reaction

Short answer

In a nuclear reaction, the main quantities conserved are lepton and baryon numbers, and mass-energy. Lepton and baryon numbers differentiate particles in particle physics and must remain constant throughout the reaction. Mass-energy conservation is based on Einstein's equation \(E = mc^2\), stating that mass and energy are interchangeable, and the total mass-energy remains constant before and after the reaction.

Step-by-step solution

Conserved Quantities in Nuclear Reactions

In a nuclear reaction, there are two main types of conserved quantities: 1. Lepton and Baryon Numbers 2. Mass-energy Let's discuss each conserved quantity in detail.

1. Lepton and Baryon Numbers

Lepton and baryon numbers are quantum numbers used to characterize and differentiate particles in particle physics. In nuclear reactions, these numbers are always conserved. Lepton number: Leptons are particles like electrons, muons, and neutrinos that do not experience a strong interaction force. As leptons are created or destroyed, the total lepton number of a nuclear reaction remains constant. For example, in beta decay, an electron (a lepton) is emitted from the nucleus, but the total lepton number is conserved. Baryon number: Baryons are particles like protons and neutrons that feel the strong nuclear force. As protons and neutrons enter or leave a nucleus, the total baryon number must also be conserved. For example, during alpha decay, a nucleus emits two neutrons and two protons, but both the initial and final nuclei have the same baryon number.

2. Mass-Energy conservation

Mass-energy in a nuclear reaction is also conserved while any system is undergoing the reaction. This means that the total mass-energy before the reaction is equal to the total mass-energy after the reaction. Mathematically, this can be represented as: \[E_{initial} = E_{final}\] This concept is based on Albert Einstein's famous equation \(E = mc^2\), which states that mass and energy are interchangeable. In nuclear reactions, some mass is converted into energy, and this energy is released as kinetic energy, radiation, or heat. But, overall, the sum of all masses and energies remains constant in a nuclear reaction. For example, in nuclear fission, a heavy nucleus splits into two smaller nuclei and releases a large amount of energy, but the mass-energy is conserved throughout the process. In conclusion, the conservation of lepton and baryon numbers and the conservation of mass-energy are the main quantities that must be conserved when balancing a nuclear reaction.