11TH GRADE · NUCLEAR PHYSICS

Atomic nucleus and radioactivity

Nuclear composition, mass defect, binding energy and decay law.

32 minutes28 theory cards

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LESSON MATERIAL

Basic Concepts

4

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.

LESSON MATERIAL

Physical quantities

13

Mass number

A

The total number of protons and neutrons in the nucleus.

Unit: dimensionless quantity

Number of protons

Z

Number of protons and charge number of the nucleus.

Unit: dimensionless quantity

Number of neutrons

N

The number of neutrons in the nucleus.

Unit: dimensionless quantity

Communication energy

E_{\text{sv}}

The energy required to split a nucleus into nucleons.

Unit: joule · $\mathrm{Dzh}$

Mass defect

\Delta m

The difference between the sum of the nucleon masses and the mass of the nucleus.

Unit: kilogram · $\mathrm{kg}$

Proton mass

m_p

Free proton mass.

Unit: atomic mass unit · $\mathrm{a.e.m.}$

Neutron mass

m_n

Mass of a free neutron.

Unit: atomic mass unit · $\mathrm{a.e.m.}$

Electron mass

m_e

Mass of a free electron.

Unit: atomic mass unit · $\mathrm{a.e.m.}$

Core mass

m_{\text{yad}}

Mass of the atomic nucleus.

Unit: atomic mass unit · $\mathrm{a.e.m.}$

Atomic mass

m_{\text{at}}

Mass of a neutral atom.

Unit: atomic mass unit · $\mathrm{a.e.m.}$

Number of undecayed nuclei

N

The number of radioactive nuclei at the current moment.

Unit: dimensionless quantity

Initial number of cores

N_0

The number of radioactive nuclei at the initial moment.

Unit: dimensionless quantity

Half-life

T

The time during which, on average, half of the original nuclei decay.

Unit: second · $\mathrm{s}$

LESSON MATERIAL

Lesson formulas

11

Alpha particle

{}^{4}_{2}\mathrm{He}

An alpha particle is a helium nucleus with two protons and two neutrons.

Beta particle

{}^{0}_{-1}\mathrm{e}

A beta minus particle is an electron emitted during a nuclear transformation.

Gamma quantum

{}^{0}_{0}\mathrm{\gamma}

A gamma quantum is a high-energy photon with no electrical charge.

Mass number composition

A=Z+N

The mass number is equal to the sum of protons and neutrons.

Number of neutrons

N=M-Z

The number of neutrons is equal to the mass number minus the number of protons.

Binding energy through mass defect

E_{\text{sv}}=\Delta mc^2

The binding energy is equal to the mass defect multiplied by the square of the speed of light.

Binding energy in megaelectronvolts

E_{\text{sv}}=\Delta m\cdot931\,\mathrm{MeV}

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

\Delta m=Zm_p+Nm_n-m_{\text{yad}}

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

m_p=1{,}00728\,\mathrm{a.e.m.},\quad m_n=1{,}00866\,\mathrm{a.e.m.},\quad m_e=0{,}00055\,\mathrm{a.e.m.}

The tabulated particle masses are given in atomic mass units.

Nuclear mass via atomic mass

m_{\text{yad}}=m_{\text{at}}-Zm_e

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

N=N_0\cdot2^{-t/T}

The number of undecayed nuclei is halved for each half-life.

DIRECTORY

Related formulas

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PRACTICE

Tasks on the topic

Nuclear physics11 class · 14 problems