- Before Einstein, mass and energy were considered separate and independently conserved quantities.
- Einstein showed that mass and energy are related by the equation
E = mc2
called Einstein’s mass–energy relation. - A small loss of mass produces a large amount of energy because c2 is very large.
- Conservation of mass and conservation of energy are unified into a single law of conservation of mass–energy.
Definitions [5]
Definition: Pair Annihilation
Whenever an electron and a positron come very close to each other, they annihilate each other by combining together and two y photons (energy) are produced. This phenomenon, in which mass is converted into energy, is called 'pair-annihilation'.
Definition: Mass Defect
The difference between the sum of the masses of the nucleons constituting a nucleus and the rest-mass of the nucleus is called ‘mass defect'.
Definition: Binding Energy
The binding energy (BE) of a nucleus is defined as the minimum energy required to separate its nucleons and place them at rest at infinite distance apart.
Definition: Binding Energy per Nucleon
Binding energy per nucleon is defined as the average energy required to remove a nucleon from the nucleus to infinite distance. Higher the binding energy per nucleon, greater is the stability of the nucleus.
Definition: Pair Production
When an energetic γ-ray photon falls on a heavy substance, it is absorbed by some nucleus of the substance and its energy gives rise to the production of an electron and a positron. This phenomenon, in which energy is converted into mass, is called 'pair-production'.
Formulae [1]
Formula: Binding Energy Formula
\[E_{b}=\left[Zm_{\mathrm{H}}+(A-Z)m_{n}-m(_{Z}X^{A})\right]c^{2}\]
Key Points
Key Points: Binding Energy Curve
- The binding energy curve is a plot of average binding energy per nucleon versus mass number (A).
- The curve has a maximum around A = 50 to 80 (about 8.5 MeV per nucleon); hence, nuclei like Fe⁵⁶ are the most stable.
- For very heavy nuclei (A > 80), the binding energy per nucleon decreases, so such nuclei, such as uranium, are less stable and may be radioactive.
- For very light nuclei (A < 20), the binding energy per nucleon is also low, so they are comparatively less stable.
- Energy is released when heavy nuclei split (nuclear fission) or when light nuclei combine (nuclear fusion) because the binding energy per nucleon increases in both cases.
Key Points: Mass-Energy Relation
