Question

In the mass of an atomic nucleus greater or less than the sum of the masses of the nucleons composing it? Why don't the nucleon masses add up to the total nuclear mass?

Short answer

The nucleus's mass is less due to binding energy and mass defect.

Step-by-step solution

Understanding the Question

The question asks whether the mass of an atomic nucleus is greater or less than the sum of the individual masses of the nucleons (protons and neutrons). It also asks for an explanation of why the masses don't add up perfectly.

Concept of Mass Defect

The mass of an atomic nucleus is actually less than the sum of the masses of the individual nucleons. This difference is known as the 'mass defect.' The mass defect is the amount by which the mass of an atomic nucleus is less than the sum of the masses of its constituent protons and neutrons.

Introduction to Binding Energy

The mass defect arises because energy is released when nucleons come together to form a nucleus. According to Einstein's equation, \[ E=mc^2 \]this energy equates to a loss in mass. The energy required to hold the nucleus together is known as the binding energy.

Conclusion: Resulting Nuclear Mass

In essence, the mass of a nucleus is less than the total mass of its nucleons due to the binding energy that holds the nucleus together. The energy required to bind the nucleons into a nucleus results in a corresponding loss of mass, leading to the nucleus having less mass than the separate nucleons.

Key concepts

Atomic Nucleus

The atomic nucleus is the heart of an atom. It is a tiny, dense region located at the center of an atom and is composed mainly of protons and neutrons, known collectively as nucleons. Each element's identity depends on the number of protons within its nucleus, called the atomic number, while the sum of protons and neutrons gives the mass number.
The nucleus accounts for nearly all of an atom's mass but occupies an incredibly small part of its volume.

• The nucleus is held together by the nuclear force, which is a strong force that acts between nucleons.
• Despite protons repelling each other due to their positive charge, the nuclear force dominates at the short distances present in the nucleus, keeping it intact.

Understanding the intricacies of the atomic nucleus helps explain why the mass of a nucleus is less than the sum of its individual nucleons.

Binding Energy

Binding energy is a crucial concept in nuclear physics. It is the energy required to separate a nucleus into individual protons and neutrons. When nucleons come together to form a nucleus, energy is released, leading to a lower energy state. This released energy results in a mass defect, explaining why a nucleus weighs less than the sum of its parts.

• Binding energy reflects the stability of a nucleus; the more binding energy per nucleon, the more stable the nucleus.
• The strong nuclear force provides this binding energy, overcoming the electrostatic repulsion between protons.

The binding energy not only stabilizes nuclei but also directly affects their mass through the mass-energy equivalence principle. This principle is beautifully demonstrated by Einstein's equation.

Einstein's Equation

Einstein's equation, represented as \[ E=mc^2 \] plays a vital role in explaining the mass defect and binding energy concepts. It states that mass and energy are interchangeable – they are two sides of the same coin.

• The equation shows that energy (\( E \) ) is equivalent to mass (\( m \) ) times the speed of light (\( c \) ) squared.
• When nucleons bind together, the resulting nucleus is lighter than the sum of individual nucleons because the binding energy is released.
• This lost mass has been converted into energy, which in turn ensures the cohesion of the nucleus.

Einstein's equation allows us to understand how nuclear reactions can release tremendous amounts of energy, as even small amounts of mass can convert to large energy quantities due to the speed of light being a very large number.