Binding energy

•sketch the variation of binding energy per nucleon with nucleon number. •explain what is meant by nuclear fusion and nuclear fission. •explain the relevance of binding energy per nucleon to nuclear fusion and to nuclear fission. •Solve problems involving mass defect and binding energy.

Summary

• Discussion: Introducing mass defect and atomic mass units. (10 minutes)

• Discussion: Mass defect and binding energy (10 minutes)• Worked example: Calculating binding energy. (10 minutes)• Student questions: Calculations. (20 minutes)• Discussion: Fission and fusion linked to binding energy

graph. (10 minutes)• Reading and further questions

Gneed two nough

• 1 Students must be familiar with the units MeV c −2 and GeV c −2

for mass.• 2 Students should be familiar with

binding energies plotted as positive quantities.

Notice anything?

• proton mass, mp = 1.673 10-27 kg

• neutron mass, mn = 1.675 10-27 kg• mass of a helium nucleus = 6.643 10-27 kg• The mass of a nucleus is less than the sum of

the masses of its parts; this is true for all nuclides.

• So much for conservation of mass.

Atomic mass units

• the atomic mass unit (amu, or u) is a convenient unit of nuclear mass.

• 1 amu or 1 u = 1/12 the mass of a neutral 12C atom (i.e. including its six electrons) = 1.66056 10-27 kg. Thus:

• mp = 1.0073 u

• mn = 1.0087 u

• me = 0.00055 u• mass of a neutral helium atom = 4.0026 u

Mass defect and binding energy• What has happened to the missing mass – or mass defect – between

the whole and the sum of the parts? • To separate the particles, they must be pulled apart against the

attractive strong force. They thus have potential energy when they are separated.

• When the particles come together to form a nucleus, their potential energy decreases.

• So energy must be put in to separate the nucleons of a nucleus.• This energy is known as the binding energy, • This does not mean that energy is required to bind nucleons together. • As with chemical bonds, this is the opposite of the truth. Energy is

needed to break bonds.

That equation

• Einstein’s Special Theory of Relativity (1905) relates mass and energy via the equation E = mc2 (where c is the speed of light in a vacuum). In this case, we have:

• binding energy = mass defect c2 or ΔE = Δ m c2

Talking about mass and energy

• It is not advisable to talk about mass being ‘converted to energy’.

• It is better to say that, in measuring an object’s mass, we are determining its energy.

• A helium nucleus has less mass than its constituent nucleons; in pulling them apart, we do work and so give them energy; hence their mass is greater.

Calculating binding energy• mp = 1.0073 u

• mn = 1.0087 u

• me = 0.00055 u• mass of a neutral helium atom = 4.0026 u

• Calculate the mass defect and binding energy for A neutral helium atom.

• Mass defect = (2mp+2mn+2me) – mHe

• Mass defect = (2.0146+2.0174+.00110) – 4.0026• Mass defect = 0.0305• binding energy = 0.0305 x 1.661 x10-27

• 4.56 10-12 J

Another way• mp = 1.0073 u

• mn = 1.0087 u

• me = 0.00055 u

• mass of a neutral helium atom = 4.0026 u• Mass defect = (2mp+2mn+2me) – mHe

• Mass defect = (2.0146+2.0174+.00110) – 4.0026• Mass defect = 0.0305• From data booklet 1u = 931.5 MeVc-2

• E = mc2

• E = (931.5 x 0.0305) x c2

• E = 28.411 MeV ……. Check 4.546x10-12

Tu du

• Complete changing energy changing mass worksheet.

• Use the spreadsheets to investigate binding energies and binding energies per nucleon

Using a spreadsheet

• On the website you can find a spreadsheet to do these calculations for you.

• Student activity: Spreadsheet calculations. (20 minutes)

• Student activity: Spreadsheet calculations of binding energy per nucleon. (20 minutes)

Binding energy per nucleon

0 20 40 60 80 100 120 140 160 180 200 220 240

Mass number (A)

Energy released by fission

Energy released by fusion

Bind

ing energy per nucleon (M

eV)

Meaning of the graph• The part of the curve to the left shows that two light elements can

produce energy by joining together - fusion • The part of the curve to the right shows that a heavy element can

produce energy by breaking in to smaller pieces - fission. • If a reaction takes place where the products are closer to the peak

than the original nucleus (nuclei) then energy is given out.• For helium the binding energy per nucleon is 28.3/4 = 7.1 MeV.• The helium nucleus has a high binding energy per nucleon and is

more stable than some of the other nuclei close to it in the periodic table.

• A very useful web site containing a huge nuclear database is to be found at:

• http://nucleardata.nuclear.lu.se

Reading and Further questions

• Adams and Allday P 374 +5q 1-5• For fun

http://www.invisiblemoose.org/ald/site_material/WALTA/Cosmic_Rays_CD/support_material/detectors/bubble_chamber/www.lalanet.gr.jp/nsm/E-radiation.html