Question

Range of weak nuclear force is (a) \(10^{-15} \mathrm{~m}\) (b) \(10^{-14} \mathrm{~m}\) (c) \(10^{-18} \mathrm{~m}\) (d) \(10^{-20} \mathrm{~m}\)

Short answer

The range of the weak nuclear force is (c) \(10^{-18} m\), as it is determined by the force carrying particles W and Z bosons and aligns with its short-range characteristic.

Step-by-step solution

Definition of Weak Nuclear Force

The weak nuclear force, also known as the weak force or the weak interaction, is one of the four fundamental forces of nature. It is responsible for certain types of particle decay processes, like beta decay. The weak force is much weaker than the strong nuclear force and the electromagnetic force but is stronger than gravity.

Comparing the Given Options

To find the correct range, we need to compare the given options and see which one fits best with the weak nuclear force's properties. (a) \(10^{-15} m\) (b) \(10^{-14} m\) (c) \(10^{-18} m\) (d) \(10^{-20} m\)

Finding the Range of Weak Nuclear Force

The range of the weak nuclear force is determined by the distance over which its effects can be felt, which is influenced by the force carrying particle called the W and Z bosons. In general, the weak nuclear force has a very short range, around \(10^{-18} m\) or \(0.001 nm\). This fact helps us narrow down the given options.

Selecting the Correct Answer

Based on the information about the range of weak nuclear force, we can select the correct answer from the given options: (a) \(10^{-15} m\): This range is too large for the weak nuclear force. (b) \(10^{-14} m\): This range is also too large, although it's closer to the correct answer. (c) \(10^{-18} m\): This range is in line with the characteristics of the weak nuclear force, making it the correct answer. (d) \(10^{-20} m\): This range is too small for the weak nuclear force. Therefore, the correct answer is (c) \(10^{-18} m\).

Key concepts

Fundamental Forces of Nature

The universe is governed by four fundamental forces that shape its structure and behavior. These forces include gravity, electromagnetism, the strong nuclear force, and the weak nuclear force. Each force has unique properties and governs different aspects of the physical world.

• Gravity: This is the force of attraction between objects with mass. It's the weakest of the four forces but acts over infinite distances, shaping planetary orbits and galaxies.
• Electromagnetism: Responsible for electricity, magnetism, and light, this force affects charged particles and also operates over long distances.
• Strong Nuclear Force: This is the most potent force, holding the nuclei of atoms together by binding protons and neutrons.
• Weak Nuclear Force: The least intuitive, this force enables certain types of particle transformations and decays, a key player in nuclear reactions occurring in stars.

Understanding these forces helps explain a wide range of natural phenomena, from the behavior of subatomic particles to the expansion of the universe.

Beta Decay

Beta decay is a fascinating process where an unstable atomic nucleus transforms into a more stable one by changing a neutron into a proton, or vice versa. This happens through the action of the weak nuclear force. There are two main types of beta decay: beta-minus and beta-plus.

• Beta-minus Decay: A neutron turns into a proton, releasing an electron and an antineutrino.
• Beta-plus Decay: A proton converts into a neutron, emitting a positron and a neutrino.

This process not only changes the identity of the atom (since protons determine the element) but also demonstrates how the weak force is unique in its ability to change quarks—the particles that make up protons and neutrons. In essence, beta decay is a crucial mechanism by which elements can transform at the nuclear level.

W and Z Bosons

The weak nuclear force is mediated by particles known as W and Z bosons. These bosons are the force carriers, or mediators, responsible for the weak interaction in particle physics.

• W Bosons: There are two types: W+ and W- bosons. They carry either positive or negative charge and are crucial in facilitating processes like beta decay.
• Z Bosons: These are neutral particles. They play a role in neutral current interactions, where particles exchange momentum and energy without changing charge.

The high mass of these bosons is a primary reason why the weak force is so short-ranged compared to others like electromagnetism. These bosons' mass limits the force's effective range, confining it to subatomic scales.

Range of Forces

Different forces in nature have varying ranges over which they exert influence. The range of a force indicates how far its effects can reach.

• Gravity: This force acts over infinite distances, although it weakens with increasing separation between masses.
• Electromagnetic Force: Like gravity, it is long-ranged and can act over vast distances, shaping atomic and molecular structures.
• Strong Nuclear Force: Though extremely powerful, its range is very short, limited to the diameter of atomic nuclei.
• Weak Nuclear Force: This force has an even shorter range, approximately 10^-18 meters, due to the mass of W and Z bosons limiting its action to subatomic scales.

Understanding the range of these forces provides insight into their roles at different scales—from holding atoms together to governing the dynamics of stars and galaxies.