Topicmda372fceaaf4d11e_1528449000663_0Topic

Why the nucleus is stable - mass defect and binding energy

Levelmda372fceaaf4d11e_1528449084556_0Level

Third

Core curriculummda372fceaaf4d11e_1528449076687_0Core curriculum

XI. Nuclear physics. The student:

6) applies the principle of energy conservation to the description of nuclear reactions; uses the terms binding energy and mass defectmass defectmass defect; calculates these quantities for any isotope.

Timingmda372fceaaf4d11e_1528449068082_0Timing

45 minutes

General learning objectivesmda372fceaaf4d11e_1528449523725_0General learning objectives

Applies the principle of energy conservation to the description of nuclear reactions.

Key competencesmda372fceaaf4d11e_1528449552113_0Key competences

1. Uses the terms binding energybinding energybinding energy and mass defect.

2. Determines binding energy and mass defect for any isotope.

Operational (detailed) goalsmda372fceaaf4d11e_1528450430307_0Operational (detailed) goals

The student:

- explains the terms binding energy and mass defect,

- calculates binding energy and mass defect for any isotope.

Methodsmda372fceaaf4d11e_1528449534267_0Methods

1. Discussion.

2. Experience.

Forms of workmda372fceaaf4d11e_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmda372fceaaf4d11e_1528450127855_0Introduction

The students remind what the structure of nucleusnucleusnucleus is and draw a corresponding diagram on the board.

What structure a nucleus has?

Proceduremda372fceaaf4d11e_1528446435040_0Procedure

The teacher introduces units used commonly in nuclear physics.

Atomic mass unit:
Masses of proton, neutron and electron are often given in terms of an atomic mass unit, where one atomic mass unit (u) is defined as $\frac{1}{12}-th$ the mass of a carbon ${}_{}{}^{12}C$ atom.
In nuclear physics the energy is often expressed in electronovolt, where 1 eV = 1,6 ∙ 10Indeks górny -19^-19 J. By applying the Einstein law on the equivalence of mass and energy, the mass can be expressed as $m=\frac{E}{c^2}$, hence $1\frac{MeV}{c^2}=1,78\cdot {10}^{-30}$ kg.

[Table 1]

The teacher discusses the quantities describing the properties of nucleusnucleusnucleus.

Mass defectmass defectMass defect:
A nucleus consists of protons and neutrons, called commonly nucleons.
The original mass of nucleusnucleusnucleus is found to be less than the sum of individual masses of its constituents. Mass defect which is the difference between the sum of the masses of the nucleus constituents and its mass, is equivalent to the energy released during the formation of nucleus.

[Interactive graphics]

The mass defect is given by the formula:

where: 
mIndeks dolny p_p - proton mass, 
mIndeks dolny n_n - neutron mass, 
mIndeks dolny nucleus_nucleus - mass of nucleus.

The students apply the formula describing the mass defectmass defectmass defect in the exercise.

Task 1

${}_2{}^{4}He$ is the most abundantabundantabundant isotope of helium. Its mass is 6,6447 ∙ 10Indeks górny -27^-27 kg. What is the mass defect?

Answer:

Mass of constituents m = 2p + 2n where:

m = 6,6950 ∙ 10Indeks górny -27^-27 kg,

mass defect: Δm = 6,6950 ∙ 10Indeks górny -27^-27 kg – 6,6447 ∙ 10Indeks górny -27^-27 kg = 5,03 ∙ 10Indeks górny -29  Indeks górny koniec^-29 kg.

Binding energybinding energyBinding energy:
The nuclear binding energy accounts for the noticeable difference between the actual mass of nucleus and its expected mass. This is the energy necessary to hold the nucleus together.

According to the Einstein's law of conversion of mass to energy the binding energy of nucleus is given as:

where: 
Δm - the mass defect, 
c - the speed of the light.

To predict stabilitystabilitystability of nucleusnucleusnucleus binding energy per nucleonnucleonnucleon is often used:

where:
A - mass number of the given kernel.

The binding energy per nucleon is the amount of energy that must be delivered to the nucleus to extract one nucleon from it. If you want to obtain independent free particles instead of a nucleus, you should provide energy equal to the total binding energy.

In the graph the binding energy per nucleon as a function of mass number is presented. 

- The average binding energy per nucleon is about 8 MeV. Only the lighter nuclei have smaller binding energy per nucleon.
- The maximum binding energy per nucleon is at A about 50. The iron nucleus is located near the maximum. Its binding energy per nucleon is 8,8 MeV making it one of the most stable nuclide.
- Nuclei with very low or very high mass numbers have smaller binding energy per nucleon and are less stable. mda372fceaaf4d11e_1527752256679_0- The average binding energy per nucleon is about 8 MeV. Only the lighter nuclei have smaller binding energy per nucleon.
- The maximum binding energy per nucleon is at A about 50. The iron nucleus is located near the maximum. Its binding energy per nucleon is 8,8 MeV making it one of the most stable nuclide.
- Nuclei with very low or very high mass numbers have smaller binding energy per nucleon and are less stable. 

[Illustration 1]

The students solve simple problems.

Task 2

Calculate binding energybinding energybinding energy of the nuclide ${}_5^{10}B$ where the mass of its nucleusnucleusnucleus is 10,0129 u. Write the result in J and MeV.

Answer:

Total mass of nucleons m = 5p + 5n = 10,079705 u.

Δm = 0,066805 u = 1,1093 ∙ 10Indeks górny -28^-28 kg.

ΔE = ΔmcIndeks górny 2² = 9,9836 ∙ 10Indeks górny -12^-12 J = 624 MeV.

Lesson summarymda372fceaaf4d11e_1528450119332_0Lesson summary

Mass defect which is the difference between the sum of the masses of the nucleus constituents and its mass, is equivalent to the energy released during the formation of nucleus. Binding energy is energy required to separate the protons and neutrons of an atomic nucleus.mda372fceaaf4d11e_1527752263647_0Mass defect which is the difference between the sum of the masses of the nucleus constituents and its mass, is equivalent to the energy released during the formation of nucleus. Binding energy is energy required to separate the protons and neutrons of an atomic nucleus.

Selected words and expressions used in the lesson plan

mass defectmass defectmass defect

binding energymass defectbinding energy

averageaverageaverage

conservation lawconservation lawconservation law

stabilitystabilitystability

nucleusnucleusnucleus

nucleonnucleonnucleon

abundantabundantabundant