Nucleus (protons and neutrons)
The atom orbiting electrons

Nuclide notation
Nucleon number (A) = number of protons and neutrons
Neutron number (N) = A - Z
7
3
Li
Proton number (Z) = number of protons

Isotopes
It is possible for the nuclei of the same element to have different numbers of neutrons in the nucleus (but it must have the same number of protons)
3
7
Li
3
6
Li

Isotopes
For example, Lithium atoms occur in two forms,
Lithium-6 and Lithium-7
3 neutrons
4 neutrons
3
7
Li
3
6
Li

Isotopes of Hydrogen

How do we know the structure of the atom?

The famous Geiger-Marsden Alpha scattering experiment
In 1909, Geiger and Marsden were studying how alpha particles are scattered by a thin gold foil.
Thin gold foil
Alpha source

Geiger-Marsden
As expected, most alpha particles were detected at very small scattering angles
Thin gold foil
Small-angle scattering
Alpha particles

Geiger-Marsden
To their great surprise, they found that some alpha particles (1 in 20 000) had very large scattering angles
Thin gold foil
Small-angle scattering
Alpha particles
Large-angle scattering

Explaining Geiger and Marsdens’ results
The results suggested that the positive (repulsive) charge must be concentrated at the centre of the atom. Most alpha particles do not pass close to this so pass undisturbed, only alpha particles passing very close to this small nucleus get repelled backwards (the nucleus must also be very massive for this to happen).
nucleus

Rutherford did the calculations!
Atomic nucleus had a diameter of about 10 -15 m
That’s 100,000 times smaller than the size of an atom (about 10 -10 meters ).

Stadium as atom
If the nucleus of an atom was a ping-pong ball, the atom would be the size of a football stadium (and mostly full of nothing)!
Nucleus
(pingpong ball

Forces in the Nucleus

Coulomb Force in Nucleus
• Repulsive force between protons
+
+

The Strong Force
The nucleons (protons and neutrons) in the nucleus are bound together by the strong nuclear force

Strong Force
• Acts over short distances (10 -15 m)
• Acts only between adjacent particles in the nucleus
• Carried by “gluons”

Why is a nucleus unstable?
Because of the relative numbers of p and n
Ex. Uranium 235
Hi! I’m uranium-235 and I’m unstable. I really need to lose some particles from my nucleus to become more stable.

The unstable nucleus emits a particle to become stable
Weeeeeeeeeeeeee!
Thus, the atom (nucleus) has decayed.

Decay of an Unstable Nucleus
1. Random –
It’s going to happen, but when?!
2. Spontaneous –
Not affected by temperature, pressure etc.
Weeeeeeeeeeeeee!

Becquerels (Bq)
• The amount of radioactivity given out by a substance is measured in Becquerels .
• One Becquerel is one particle emitted per second.

How to detect particles?
• Photographic film
• Fluorescence
• Geiger-Müller tube (GM tube) connected to a counter (counts the # of particles)
– Use filters to distinguish alpha, beta, and gamma particles

Three main types of particles can be ejected from an unstable nucleus
.

Alpha particles

Alpha particles
• 2 protons and 2 neutrons joined together
– Helium nucleus
• Stopped by paper or a few cm of air
• Highly ionising
• Deflected by electric and strong magnetic fields
4
2
α 4
2
He
2+

Alpha Decay
Atomic mass goes down by 4
235
92
U
231
90
Th
Atomic number goes down by 2
+
2
4
He
2+

Alpha Decay
Atomic mass goes down by 4
235
92
U
231
90
Th
Atomic number goes down by 2
+
4
2
α

Beta particles

Beta particles
• Fast moving electrons or positrons
• Stopped by about 3 mm of aluminium
• Weakly ionising
• Deflected by electric and magnetic fields
0
-1
0
-1
Beta Negative  electron
0
+1
0
+1
Beta Positive  Positron

Beta decay
• In the nucleus a neutron [or proton] changes into an electron [positron] (the beta particle which is ejected) and a proton [neutron] (which stays in the nucleus) and an antineutrino [neutrino]
– During beta decay the mass number stays the same but the proton number goes up [or down] by 1.
46
20
Ca
40
19
K
46
21
Sc +
0
-1
0
+
ע e 0 antineutrino
40
18
Ar +
0
+1
+ 0
ע e
0 neutrino

Beta decay
• In the nucleus a neutron [or proton] changes into an electron [positron] (the beta particle which is ejected) and a proton [neutron] (which stays in the nucleus) and an antineutrino [neutrino]
– During beta decay the mass number stays the same but the proton number goes up [or down] by 1.
46
20
Ca
40
19
K
46
21
Sc +
0
-1
+
0 ע e 0 antineutrino
40
18
Ar +
0
+1
+
0 ע e
0 neutrino

Gamma rays

Gamma rays
• High frequency electromagnetic radiation
• Stopped by several cm of lead
• Very weakly ionising
• NOT affected by electric or magnetic fields

Gamma rays
Usually associated with alpha decay
Excited nucleus relaxes by releasing a gamma ray.
235
92
U
231
Th
*
90
+
α
231
Th
90
+

Biological Effects of
Localized Radiation Exposure
• Short Term
– Low dosage – skin reddening
– High dosage – skin or tissue necrosis
• Long Term – through direct or indirect actions
– Damages or mutates DNA and other cells
(specific concern: somatic cells)
– Potential cancer causing

Best Practice: Prevention!
• Limit Radiation Concentration (in labs)
• Limit Exposure Time
• Increase Distance
• Use Appropriate Shielding Materials

½ - life
• The decay of a single nuclei is totally random
• However, with large numbers of atoms a pattern does occur

½ - life
• This is the time it takes half the nuclei to decay
Number of nuclei undecayed half-life (t ½ ) time

½ - life
• This is the time it takes half the nuclei to decay
Number of nuclei undecayed time half-life (t ½ )

½ - life
• This is the time it takes half the nuclei to decay
Number of nuclei undecayed
A graph of the count rate against time will be the same shape time half-life (t ½ )

Different ½ - lives
• Different isotopes have different half-lives
• The ½-life could be a few milliseconds or
5000 million years!
Number of nuclei undecayed time half-life (t ½ )

Decay Constant ( λ)
• The probability that an atom will decay
– Remember that the decay of a single nuclei is totally random
• Activity = the decay constant times the number of atoms
– Equation  A = λ N

Determining ½ - lives
• For short half-lives
– Use a GM-tube to measure initial activity, and then measure the time it takes for that activity to decrease by a half.
– That time is the half-life!
• For long half-lives
– Use a GM-tube to measure the initial Activity
– Measure the mass of the sample
• Calculate the # of atoms using molar mass and Avogadro’s number
– Calculate λ [decay constant] from A
0
– Calculate half-life  t
1/2
= ln(2) / λ
= λ N
0

Nuclear Reactions

Unified mass unit (u)
• Defined as 1/12 of the mass of an atom of
Carbon-12 u = 1.6605402 x 10 -27 kg

Energy mass equivalence
• E = mc 2
• E = 1.6605402 x 10 -27 x (2.9979 x 10 8 ) 2
• E = 1.4923946316 x 10 -10 J
• Remembering 1 eV = 1.602177 x 10 -19 J
• 1 u = 931.5 MeV
• The electron-Volt is a convenient unit of energy for nuclear physics

Mass defect
For helium, the mass of the nucleus =
4.00156 u
But, the mass of two protons and two nuetrons = 4.0320 u!!!!
Where is the missing mass?

Mass defect
The missing mass ( mass defect ) has been stored as energy in the nucleus. It is called the binding energy of the nucleus.
It can be found from E = m c 2

Mass defect calculation
• Find the mass defect of the nucleus of gold, 196.97 - Au

Mass defect calculation
• The mass of this isotope is 196.97
u
• Since it has 79 electrons its nuclear mass is 196.97u – 79x0.000549u = 196.924u

Mass defect calculation
• The mass of this isotope is 196.97
u
• Since it has 79 electrons its nuclear mass is 196.97u – 79x0.000549u = 196.924u
• This nucleus has 79 protons and 118 neutrons, individually these have a mass of 79x1.0007276u + 118x1.008665u =
198.080u

Mass defect calculation
• The mass of this isotope is 196.97
u
• Since it has 79 electrons its nuclear mass is 196.97u – 79x0.000549u = 196.924u
• This nucleus has 79 protons and 118 neutrons, individually these have a mass of 79x1.0007276u + 118x1.008665u =
198.080u
• The difference in mass (mass defect) is therefore 1.156u

Mass defect calculation
• The difference in mass (mass defect) is therefore 1.156u
• This “missing mass” is stored as energy in the nucleus (binding energy).
• 1u is equivalent to 931.5 MeV

Nuclear Reactions
Similar calculation as mass defect – the products have less mass that the reactants, and the lost mass is converted into KE of the products
Transmutation - the conversion of the nucleus of one isotope or element into another
Artificial (induced) transmutation – the energy required for transmutation is provided by
“artificial” means

EX. Artificial Transmutation – bombard a nitrogen atom with a high E alpha particle
7
14
N
7
14
N
+
4
2
4
+
2
2+
8
17
O
8
17
O
+
1
1 p
+
1
1 p

Binding energy
The work (energy) required to completely separate the nucleons of the nucleus.

Binding energy per nucleon
The BE / nucleon number
- the work (energy) required to completely remove 1 nucleon from a nucleus
It is a measure of how stable the nucleus is.

The binding energy curve

Let’s do some reading!

Nuclear Fission

Uranium
Uranium 235 has a large unstable nucleus.

Capture
A lone neutron hitting the nucleus can be captured by the nucleus, forming Uranium 236.

Fission and free neutrons
Uranium 236 is very unstable and splits
(nuclear fission ) into two smaller nuclei
(called daughter nuclei ) and three neutrons (with lots of kinetic energy )

Fission
These free neutrons can strike more uranium nuclei, causing them to split.

Chain Reaction
If there is enough uranium ( critical mass ) a chain reaction occurs. Huge amounts of energy are released very quickly.

Chain Reaction
If there is enough uranium (critical mass) a chain reaction occurs. Huge amounts of energy are released very quickly.

Bang!
This can result in a nuclear explosion!
(movie is of a 23 ktonne nuke detonated underwater.) http://www.youtube.com/watch?v=b2WQvtGnBQw

Nuclear fusion – Star power!

Nuclear fusion – Star power!
• http://hyperphysics.phyastr.gsu.edu/hbase/nucene/fusion.html#c1
• http://hyperphysics.phyastr.gsu.edu/hbase/astro/astfus.html#c1
• Check out the 2 links above to better understand all the types of nuclear reactions that occur in stars.

The binding energy curve