Question

A free neutron is unstable and decays into a proton with a half-life of \(10.4\) min. (a) What other particle forms? (b) Why don't neutrons in atomic nuclei decay at the same rate?

Short answer

(a) When a free neutron decays into a proton, an electron (\(e^-\)) and an anti-electron neutrino (\(\bar{\nu}_e\)) are also formed. (b) Neutrons within atomic nuclei don't decay at the same rate as free neutrons because of the nuclear binding energy, which stabilizes the protons and neutrons inside the nucleus. The decay of a neutron to a proton is energetically unfavorable in a nucleus unless the resulting nucleus has a lower energy state than the initial nucleus.

Step-by-step solution

(a) Identify the decay process for a free neutron)

In particle physics, a free neutron (n) is known to decay into a proton (p) through a process called beta decay. This decay process can be represented as: \(n \rightarrow p + e^- + \bar{\nu}_e\) Here, \(e^-\) is an electron and \(\bar{\nu}_e\) is an anti-electron neutrino.

(b) Explain why neutrons within atomic nuclei don't decay at the same rate)

Neutrons within atomic nuclei don't decay at the same rate as free neutrons due to the nuclear binding energy, which plays a crucial role in stabilizing the protons and neutrons inside the nucleus. The nuclear binding energy is the energy that is required to disassemble a nucleus into its constituent protons and neutrons. This energy helps overcome the electrostatic repulsion between the positively charged protons. When a neutron is inside a nucleus, it is in a bound state with lower energy compared to the energy of a free neutron. Conversely, a free neutron has a higher energy state, making it unstable and prone to decay. In a nucleus, the decay of a neutron to a proton is energetically unfavorable unless the resulting nucleus has a lower energy state than the initial nucleus. Thus, the decay rate of neutrons within atomic nuclei is significantly slower than that of free neutrons.

Key concepts

Beta Decay

Neutron decay is a fascinating process in particle physics known as beta decay. During beta decay, a free neutron is transformed into a proton by emitting an electron (\(e^-\)) and an antineutrino (\(\bar{u}_e\)). This process can be represented by the equation:
\[ n \rightarrow p + e^- + \bar{u}_e \]
Beta decay is crucial for understanding the stability of matter in the universe. Neutrons are uncharged particles, and without them undergoing this transformation, the universe would lack the complexity we see in atomic structures. The emitted electron is often referred to as a beta particle, which gave this decay process its name.

• Occurs due to weak nuclear force.
• Allows transformation of a neutron into a proton.
• Emits an electron and an antineutrino.

Understanding beta decay helps scientists explore how elements are formed and how they evolve over time.

Nuclear Binding Energy

Nuclear binding energy is the glue that holds the nucleus of an atom together. It's the energy required to disassemble a nucleus into its separate protons and neutrons. When particles within a nucleus are tightly bound by this energy, the nucleus becomes more stable and less likely to decay.
The importance of nuclear binding energy explains why neutrons in nuclei generally don't decay as they do when they are free. Inside a nucleus, neutrons are in a lower energy state due to the significant binding energy keeping them stable. A decay process, like that of a neutron turning into a proton, would require an energy transition to a more favorable, lower-energy state, making spontaneous decay less probable unless it's energetically favorable.

• Contributes to nuclear stability.
• Measured in mega-electron volts (MeV).
• Varies between different nuclei.

Acknowledging the role of nuclear binding energy aids in understanding processes like nuclear fission and fusion.

Particle Physics

Particle physics is the field that studies the fundamental constituents of matter, including particles like neutrons and protons, and the forces acting between them. Beta decay is an essential aspect of particle physics, showcasing the transformation of particles at a fundamental level due to the weak nuclear force.
In particle physics, understanding the interactions that lead to processes like beta decay helps clarify the behaviors of particles in various environments. For instance, the weak nuclear force, which is responsible for beta decay, operates over very short distances and is integral to processes like the sun's nuclear reactions that power its energy output.

• Focuses on subatomic particles.
• Explores fundamental forces, including the weak nuclear force.
• Helps explain particle interactions and transformations.

Particle physics provides insight into the intrinsic nature of matter, explaining complexities from simple interactions to vast cosmic events.

Nuclear Stability

Nuclear stability refers to the balance within an atomic nucleus that prevents it from spontaneously changing or decaying. The stability of a nucleus depends on the ratio of neutrons to protons and the forces that bind them together, primarily the nuclear binding energy.
Inside a nucleus, the forces at play include the strong nuclear force, which acts to hold protons and neutrons together, counteracting the electrostatic repulsion between similarly charged protons. The stability is also influenced by the energy states of particles. Neutrons in a stable nucleus are less likely to decay due to these forces and energy considerations.

• Is influenced by neutron-to-proton ratios.
• Involves the strong nuclear force and binding energy.
• Determines decay likelihood of the nucleus.

Understanding nuclear stability is pivotal for elucidating why certain isotopes are stable while others undergo radioactive decay, influencing fields from energy production to radiometric dating.