Why does a given nucleus have less mass than the sum of its constituent protons and neutrons?

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Understand that a nucleus is made up of protons and neutrons, which are collectively known as nucleons.

Recognize that when nucleons come together to form a nucleus, they release energy in the form of binding energy, which helps to hold the nucleus together.

Learn that according to Einstein's mass-energy equivalence principle, represented by the equation $E = mc^2$, energy and mass are interchangeable. Here, $E$ represents energy, $m$ represents mass, and $c$ is the speed of light in a vacuum.

Realize that the release of binding energy when a nucleus forms results in a loss of mass. This mass loss is what makes the mass of the nucleus less than the sum of the individual masses of the protons and neutrons.

Conclude that the difference in mass, known as the mass defect, is crucial for the stability of the nucleus, as it is directly related to the binding energy that holds the nucleus together.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Mass Defect

The mass defect refers to the difference between the mass of an atomic nucleus and the sum of the masses of its individual protons and neutrons. This phenomenon occurs because when nucleons (protons and neutrons) bind together to form a nucleus, some of their mass is converted into energy, as described by Einstein's equation E=mc². This energy is released during the formation of the nucleus, resulting in a lower overall mass.

Binding Energy

Binding energy is the energy required to disassemble a nucleus into its individual protons and neutrons. It is a measure of the stability of the nucleus; a higher binding energy indicates a more stable nucleus. The binding energy is directly related to the mass defect, as the energy released during nucleon binding accounts for the mass that is 'lost' when the nucleus is formed.

Nuclear Forces

Nuclear forces are the strong interactions that hold protons and neutrons together within the nucleus. These forces are much stronger than the electromagnetic forces that would otherwise cause protons to repel each other due to their positive charge. The strong nuclear force operates at very short ranges and is responsible for the stability of the nucleus, contributing to the mass defect and binding energy.

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