11TH GRADE · NUCLEAR PHYSICS
Atomic nucleus and radioactivity
Nuclear composition, mass defect, binding energy and decay law.
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Basic Concepts
Atomic nucleus
The positively charged central part of an atom, consisting of protons and neutrons.
The number of protons Z determines the chemical element, and the mass number A is equal to the sum of protons and neutrons.
Mass defect
The difference between the sum of the masses of free nucleons and the mass of the bound nucleus.
A bound nucleus is lighter than the sum of individual nucleons; the corresponding energy difference is Δmc².
Nuclear binding energy
The energy required to completely separate a nucleus into free nucleons.
The higher the specific binding energy, the more resistant the nucleus is, on average, to splitting into individual nucleons.
Radioactive decay
Spontaneous transformation of an unstable nucleus with the emission of particles or radiation.
The moment of decay of an individual nucleus is random, but for a large number of nuclei the rate of the process is accurately described by the half-life.
Physical quantities
Mass number
The total number of protons and neutrons in the nucleus.
Unit: dimensionless quantity
Number of protons
Number of protons and charge number of the nucleus.
Unit: dimensionless quantity
Number of neutrons
The number of neutrons in the nucleus.
Unit: dimensionless quantity
Communication energy
The energy required to split a nucleus into nucleons.
Unit: joule ·
Mass defect
The difference between the sum of the nucleon masses and the mass of the nucleus.
Unit: kilogram ·
Proton mass
Free proton mass.
Unit: atomic mass unit ·
Neutron mass
Mass of a free neutron.
Unit: atomic mass unit ·
Electron mass
Mass of a free electron.
Unit: atomic mass unit ·
Core mass
Mass of the atomic nucleus.
Unit: atomic mass unit ·
Atomic mass
Mass of a neutral atom.
Unit: atomic mass unit ·
Number of undecayed nuclei
The number of radioactive nuclei at the current moment.
Unit: dimensionless quantity
Initial number of cores
The number of radioactive nuclei at the initial moment.
Unit: dimensionless quantity
Half-life
The time during which, on average, half of the original nuclei decay.
Unit: second ·
Lesson formulas
Alpha particle
An alpha particle is a helium nucleus with two protons and two neutrons.
Beta particle
A beta minus particle is an electron emitted during a nuclear transformation.
Gamma quantum
A gamma quantum is a high-energy photon with no electrical charge.
Mass number composition
The mass number is equal to the sum of protons and neutrons.
Number of neutrons
The number of neutrons is equal to the mass number minus the number of protons.
Binding energy through mass defect
The binding energy is equal to the mass defect multiplied by the square of the speed of light.
Binding energy in megaelectronvolts
If the mass defect is given in atomic units, the binding energy is equal to the mass defect multiplied by 931 megaelectronvolts.
Core mass defect
The mass defect is equal to the sum of the masses of free nucleons minus the mass of the nucleus.
Masses of proton, neutron and electron
The tabulated particle masses are given in atomic mass units.
Nuclear mass via atomic mass
The mass of the nucleus is equal to the mass of the neutral atom minus the total mass of the electrons.
Law of Radioactive Decay
The number of undecayed nuclei is halved for each half-life.
Related formulas
The same formulas in the reference, with symbols and units.
Tasks on the topic
Statements, answer options and the walkthrough.