33.1 Discovery of neutrons
Evidence for a nucleus
Rutherford’s explanation
A neutral atom contains equal amounts of positive (+) and negative (-) charge . The above experiment, supervised by Ernest Rutherford in 1911, first provided evidence that an atom’s positive charge and virtually all of its mass is concentrated in one small region of the atom.
A thin piece of gold foil was bombarded with alpha particles, which are positively charged . Most of the alpha particles passed straight through the gold atoms, But a few were repelled so strongly that they bounced back or were deflected through large angles. These results led Rutherford to propose this model of the atom: a heavy, positively charged nucleus at the centre, with much lighter, negatively charged electrons in orbit around it.
33.2 Atomic number and mass number
For most elements, a sample contains a mixture of different versions. These have the same number of protons (and electrons) but different numbers of neutrons .

Nuclide,X This is any particular version of an atom. Above are simple models of the two naturally occurring nuclides of lithium, along with the symbols used to represent them.
Nucleon number or Mass Number, A As protons and neutrons are called nucleons, this is the total number of protons plus neutrons in the nucleus. It was once called the mass number.
A = Z + N
Proton number or Atomic Number,Z This is the number of protons in the nucleus (and therefore the number of electrons in a neutral atom). It was once called the atomic number.
Neutron number,N is the number of neutron in the nucleus
33.3 Isotopes
1.Isotopes of an element have the same proton number but different nucleon numbers.The nucleon numbers differ becouse the nuclei have different numbers of neutrons.
2.These are atoms with the same proton number but different nucleon numbers. They have the same electron arrangement and, therefore, the same chemical properties. The following statements illustrate the meanings of the terms element, nuclide, and isotope.
• Lithium is an element.
• Lithium-6 is a nuclide; lithium-7 is a nuclide.
• Lithium-6 and lithium-7 are isotopes.
Note:
• A nuclide is commonly referred to as ‘an isotope’, though strictly speaking, this is incorrect
33.4 Mass defect and binding energy
Atomic measurements
The unified atomic mass unit (u) is used for measuring the masses of atomic particles. It is very close to the mass of one proton (or neutron). However, for practical reasons, it is defined as follows:
1 u = mass of carbon-12 atom
12
Converting into kg, 1 u = 1.66 x 10 -11 kg. mass of proton 1.007 28 u mass of neutron 1.008 67 u mass of electron 0.000 55 u charge on proton +1.60 x 10 -19 C charge on electron -1.60 x 10 -19 C diameter of an atom ~10 -10 m diameter of a nucleus ~10 -14 m
Note:
• The proton and neutron have approximately the same mass – about 1800 times that of the electron.
• ~ means ‘of the order of i.e. ‘within a factor ten of
• The diameter of an atom is ~10 4 times that of its nucleus. (Atom size varies from element to element.)
• Confusingly, the symbol e may be used to represent the charge on an electron (-) or a proton (+). In this unit, the charge on an electron will be called -e.
Energy and mass

One conclusion from Einstein’s theory of relativity is that energy has mass. If an object gains energy, it gains mass. If it loses energy, it loses mass. The change of energy DE is linked to the change of mass
Dm(mass defect) by this equation:
DE = Dmc 2 where c is the speed of light: 3 x 10 8 m s -1 c 2 is so high that energy gained or lost by everyday objects produces no detectable change in their mass.
However, the energy changes in nuclear reactions produce mass changes which are measurable. For example, when a fast a particle is stopped, its mass decreases by about 0.2%. The mass of an object when it is at rest is called its rest mass .
With nuclear particles, energy is often measured in MeV (the electronvolt, eV, ):
1 MeV = 1.60 x 10 -13 J
From data on mass changes, scientists can calculate the energy changes taking place. With nuclear particles, mass is usually measured in u .
By converting 1 u into kg and applying DE = Dmc 2 , it is possible to show that
1 u is equivalent to 931 MeV
Mass defect
A helium-4 nucleus is made up of 4 nucleons (2 protons and 2 neutrons). The calculation above shows that the nucleus has less mass than its four nucleons would have as free particles. The nucleus has a mass defect of 0.030 40 u.
Generally Mass Defect Dm can be concluded as follows:
Dm=[Zm p
+(A-Z)m n
]-M
N m p
= mass of proton m n
= mass of neutron
M
N
= mass of nucleus
The reason for the mass defect is as follows. In the nucleus, the nucleons are bound together by a strong nuclear force. As work must be done to separate them, they must have less potential energy when bound than they would have as free particles. Therefore, they must have less mass.
All nuclides have a mass defect (apart from hydrogen-1 whose nucleus is a single proton). For example: hydrogen-2 iron-56 lead-208 uranium-238
Binding energy
Mass defect Mass defect per nucleon
0.002 40 u
0.528 75 u
1.757 84 u
1.935 38 u
0.001 20 u
0.009 44 u
0.008 45 u
0.008 13 u

The binding energy of a nucleus is the energy equivalent of its mass defect. So it is the energy needed to split the nucleus into separate nucleons. For example, a helium-4 nucleus has a mass defect of 0.030
40 u. As 1 u is equivalent to 931 MeV, 0.030 40 u is equivalent to 28.3 MeV. So the binding energy of the nucleus is 28.3 MeV.
Generally ,
Binding Energy E
B
= (mass defect) x (c 2 )
= Dm c 2
= [[Zm p
+(A-Z)m n
]-M
N
] c 2
Note:
• The term ‘binding energy’ is rather misleading. ‘Unbinding energy’ would be better. 28.3 MeV is the energy needed to ‘unbind’ the nucleons in helium-4.
Binding energy pernucleon vs nucleon number graph
The stability of a nucleus depends on the binding energy per nucleon . The graph above shows how this varies with nucleon number. The line gives the general trend; points for some individual nuclides have also been included.
Note:
• Nuclei near the ‘hump’ of the graph are the most stable, because they need most ‘unbinding energy’ per nucleon.
• A graph of mass defect against nucleon number has the same general form as the graph above.
If nucleons become rearranged so that they have a higher binding energy per nucleon, there is an output of energy.
Radioactive decay Unstable nuclei decay to form more more stable products, so energy is released. In a decay, for example, this is mostly as the kinetic energy of an a particle. When the a particle collides with atoms, it loses KE and they speed up. So radioactive decay produces heat.
Nuclear reactions The fission and fusion reactions on the next page give out energy. During fission, heavy nuclei split to form nuclei nearer the ‘hump’ of the graph. During fusion, light, nuclei fuse (join) to form heavier ones.

33.5 Mass spectrometry
Between slits S
2
and S
3
Electric force = magnetic force
(velocity selector)
After slit S
3
,
Centrifugal force = Magnetic force
Or r a m since E,B and q are constant
(the isotope’s mass can be determined)