Question

What is mass defect? How it is related to the binding energy of nucleus?

Short answer

Mass defect is the difference between the total mass of nucleons and the mass of the nucleus. It is related to the binding energy through Einstein’s equation: \( E = \text{mass defect} \times c^2 \).

Step-by-step solution

- Define Mass Defect

Mass defect is the difference between the sum of the masses of the protons and neutrons (nucleons) in a nucleus and the actual mass of the nucleus itself. Mathematically, it can be expressed as: \[ \text{Mass Defect} = \text{(Mass of Protons + Mass of Neutrons)} - \text{Mass of Nucleus} \]

- Understand Binding Energy

The binding energy of a nucleus is the energy required to disassemble it into its separate nucleons (protons and neutrons). It provides a measure of the stability of a nucleus: the higher the binding energy, the more stable the nucleus.

- Calculate Binding Energy using Einstein’s Equation

According to Einstein’s mass-energy equivalence principle, the binding energy can be calculated from the mass defect using the equation: \[ E = \text{mass defect} \times c^2 \] where \( E \) is the binding energy and \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \) m/s).

- Relation between Mass Defect and Binding Energy

The mass defect is directly related to the binding energy: when nucleons come together to form a nucleus, the mass defect represents the mass that is converted into binding energy, which holds the nucleus together.

Key concepts

headline of the respective core concept

Mass defect is a fascinating concept in nuclear physics. At its core, it is the difference between the expected mass of a nucleus and its actual mass. When you add up the masses of all the protons and neutrons (the nucleons) in a nucleus, you might think that their total mass would equal the mass of the nucleus itself. However, the actual mass of the nucleus is slightly less. This discrepancy is the mass defect.
The formula to calculate the mass defect is:
\[ \text{Mass Defect} = \text{(Mass of Protons + Mass of Neutrons)} - \text{Mass of Nucleus} \]
This difference arises because some mass is converted into energy during the formation of the nucleus. This brings us to our next concept, which is closely related to mass defect.

headline of the respective core concept

Binding energy is the energy that holds the nucleus together. It is the energy required to disassemble the nucleus into its separate protons and neutrons. The concept of binding energy explains why a nucleus remains intact instead of spontaneously splitting apart.
The binding energy is a measure of the stability of the nucleus. A higher binding energy means that more energy is needed to break the nucleus apart, which in turn implies greater stability of the nucleus.
To illustrate the concept further, think of binding energy as the 'glue' for the nucleus. Without this glue, the nucleons would drift apart. The binding energy can be precisely calculated by using the mass defect.

headline of the respective core concept

Einstein’s mass-energy equivalence principle provides the formula to convert mass defect into binding energy. This principle is encapsulated in the famous equation:
\[ E = \text{mass defect} \times c^2 \]
Here, \( E \) represents the binding energy, \( \text{mass defect} \) is the amount of mass converted into energy, and \( c \) is the speed of light in a vacuum, approximately \( 3 \times 10^8 \) meters per second.
The relation between mass defect and binding energy stems from this equation. The mass defect represents the mass that gets converted into energy (binding energy) when the nucleons combine to form a nucleus. Therefore, the binding energy calculated using this mass-energy equivalence formula tells us how much energy is needed to break the nucleus back into individual protons and neutrons.
This brilliant concept shows how mass and energy are interchangeable, marking a key discovery in modern physics.