Topic – Physics 2a

Mass defect and binding energy

• Prior learning• Atomic structure• Electrical forces• Key words

– Atomic nucleus,mass difference, mass of products, nuclear reactions, total mass

Topic – Physics 2a

Topic – Physics 2a

• Know how binding energy is linked to Einstein's equation – E=mc2

• Calculate mass difference

• Complete problem solving questions on binding energy

By the end of this lesson we should be able to:

Topic – Physics 2a

Topic – Physics 2a

What is binding energy?• Nuclei are made up of protons and neutron, but the

mass of a nucleus is always less than the sum of the individual masses of the protons and neutrons which constitute it.

• The difference (missing mass) is a measure of the nuclear binding energy which holds the nucleus together.

• This binding energy can be calculated from the Einstein relationship:

• Nuclear binding energy = Δmc2

Topic – Physics 2a

Mass defect

•The measured mass of a nucleus is always less than the sum of the individual masses of its nucleons.•This difference is called MASS DEFECT

Topic – Physics 2a

Binding energy and mass defect

• The mass defect is a measure of the atoms binding energy

• The more binding energy per nucleon the greater the atoms stability – held together stronger!!

Topic – Physics 2a

To calculate binding energy of a nucleus…

• Add the mass of the individual nucleons (protons and neutrons)

• Then subtract the mass of the actual atom itself

• The mass left over – Mass defect

Topic – Physics 2a

Values and Equation• Mass of proton 1.67262 x 10-27kg or 1.00727u• Mass of neutron 1.67493 x 10-27 kg or 1.00867u• Mass of electron 9.11 x 10-31kg or 5.49 x 10-4u• See tables/data sheet for other values of atoms

• Mass difference = mass of particles– mass of atom

Topic – Physics 2aExample: When a neutron combines with a proton

Deuteron nucleus• Neutron mass = 1.00867u• Proton mass = 1.00728u• = 2.01595u

• Deuterium nuclear mass = 2.01350u• 2.01595 – 2.01350 =• Difference (loss) = 0.00245u

Topic – Physics 2a

Converting into energy

• Constants:• 1eV = 1.6 x 10-19J• 1 MeV = 1.6 x 10-13 J• 1 u = 1.6606 x 10-27 kg• 1u = 931 MeV

• speed of light, c = 3.0 x 108 ms-1

Topic – Physics 2a

Example: converting to energy

• Mass defect is then converted into an energy equivalent

• x 931

• 0.00245u x 931 = 2.3MeV of energy• This is the energy that would be

required to pull the nucleus apart

Topic – Physics 2a

Worksheet

• Eb = md c2

where:

• Eb = the binding energy in joules (J)

• md = mass defect in kg.

• c = speed of light, 3.0 x 108 ms-1

Topic – Physics 2aExample- Calculate the binding

energy of a lithium-7 nucleus, in joules and MeV.

• mass defect = (mass of neutrons and protons) - (mass of nucleus)= [(3 x mass proton) + (4 x mass neutron)] - (mass of lithium )In kg= [(3 x 1.67 x 10-27) + (4 x 1.68 x 10-27)] - 1.165 x 10-26

= 5.01 x 10-27 + 6.72 x 10-27 - 1.165 x 10-26

= 8.0 x 10-29 kgE = Mc2

E = 8.0 x 10-29 x (3.0 x 108)2 = 7.12 x 10-12 J

In u units1 u = 1.6606 x 10-27 kg therefore8.0 x 10-29 / 1.66 x 10-27 = 0.4818 u0.4818 x 931 = 44.86MeV(check that’s correct by x 1.6 x 10-13 to get back into J)

Topic – Physics 2aIn the sun, hydrogen atoms combine to make

helium in the process of fusion. In this process, energy is released. One of the reactions is

shown. Determine the binding energy release for this reaction in joules and MeV.

Topic – Physics 2aA common reaction in nuclear fission power plants is , calculate the energy released from this

reaction in joules and MeV.

1 u = 1.6606 x 10-27 kg therefore

Topic – Physics 2a

Extension Questions1. What is the binding energy per nucleon in MeV for the following atoms involved in nuclear energy:• a. U-238 nucleus b. He-4 nucleus

c. Fe-56 (one of the most stable atoms) (Fe = 55.934939 u)

2. The oxygen atom O has an isotope, O. Find the binding energy of each nucleus and thus • determine which is more stable.

3. Calculate the energy released from one decay of U-238.

Topic – Physics 2a

Topic – Physics 2a

Topic – Physics 2a

Topic – Physics 2a

Topic – Physics 2a

links

• http://www.s-cool.co.uk/a-level/physics/nuclear-energy/revise-it/mass-defect

• http://www.colorado.edu/physics/2000/periodic_table/amu.html

• http://www.a-levelphysicstutor.com/we-nuc-binding-energy.php

Topic – Physics 2a

• Know how binding energy is linked to Einstein's equation – E=mc2

• Calculate mass difference

• Complete problem solving questions on binding energy

By the end of this lesson we should be able to:

Topic – Physics 2a