1. The constitution of nucleus
Third lecture

2. The proton-electron hypothesis of the constitution of the nucleus
Prout: suggest that all atomic weights must be integral multiples of the atomic weight of hydrogen and all elements might be built up of hydrogen . But it was found that atomic weight of some elements are fractional as Cl , Cu .
Nevertheless, so many elements have atomic weights are seemed to be some basis for Prout's hypothesis. The idea that all elements are built up from one basic substance received supports after the discovery of isotopes.
Also, It was found that most elements are mixtures of isotopes, and the different isotopes of an element have the same number and the arrangements of electrons, and consequently their spectra have the same general structure. They are distinguished from one another by their different atomic masses.

3. Aston: formulate his whole numbers rule, which is modified from Prout's hypothesis.
 According to Aston's rule:
“All atomic weights are very close to integers, and the fractional atomic weights are caused by the presence of two or more isotopes each of which has a nearly integral atomic weight”.
 The combination of the whole number rule and the properties of the hydrogen nucleus lead to assumption that atomic nuclei are built up of hydrogen nuclei, and the hydrogen nucleus was given the name proton.
The proton-electron hypothesis of nucleus seemed to be consistent with the emission of α and β particles by the atoms of radioactive elements. The interpretation of radioactivity showed that both α and β particles were ejected from the nuclei of the atoms undergoing transformation and the presence of electrons in the nucleus made it seem reasonable under same conditions, one of them might be ejected.
It was also assumed that the α-particle could be formed in the nucleus by the combination of four protons and two electrons.

4. The angular momentum of the nucleus; Failure of the proton – electron hypothesis:
One of the failures of the hypothesis was associated with an unknown property of the nucleus, the angular momentum.
The discovery that the nucleus has an angular momentum, or spin which is associated with a magnetic moment was a result of a detailed study of spectral lines.
The splitting of a spectral line into a number of lines lying close together, is called hyperfine structure.
The properties associated with the hyperfine structure are the mass and angular momentum of the nucleus.

5. The isotope effect is not enough to explain the hyperfine structure
The isotope effect is not enough to explain the hyperfine structure. The hyperfine structure can be accounted for quantitatively assuming that the nucleus has an angular momentum.
 The nuclear angular momentum is a vector, I, of magnitude
|I|= sqrt [i(i+1)] h/2π
Where i is the quantum number defines I
According to the rule
Iz = i h/2π
The value of I has been found experimentally to depend on the mass number A of the nucleus.
If A is even: I is an integer or 0,1,2,3,…
If A is odd: I is an odd half integral value 1/2, 3/2 ,5/2 ,….
 This rule leads to one of the failures of the proton-electron hypothesis.

6. Example: 7N14 Atomic no. =7 , mass no. = 14
It's nucleus would have 14 protons and 7 electrons under this hypothesis.
A =14 (even numbers) → The contribution of the protons to the angular momentum should be an integral multiple of h/2π . An electron has spin ½ ћ so the contribution of 7 electrons is an odd half integral multiple of h/2π , and the total integral momentum of nitrogen nucleus should be an odd half - integral multiple of h/2π .
But the angular momentum of nitrogen nucleus has been found experimentally to be I = 1 , an integer , In contradiction to the value obtained by the proton-electron hypothesis

7. The discovery of the neutron
Rutherford in 1920 suggested that, an electron and proton might be so closely combined as to form a neutral particle which is given the name neutron.
All the methods used for detection of P or e depend on the deflection of the charged particle by M.F or E.F. So, it is difficult to detect the nº.
Chadwick in 1932 demonstrated the existence of neutrons. This discovery led to presently accepted idea that the nucleus is built of protons and neutrons.
2He4 + 4Be9 → 6C n1
Chadwick detected the neutrons, since these particles, unlike protons, produce no tracks in the cloud chamber and no ionization in the ionization chamber.
These properties + the penetrating power of these particles show that the charge of these particles must be zero, and was identified as Rutherford's neutron.

8. The proton-neutron hypothesis
The discovery of neutron, led to the assumption that every atomic nucleus consist of protons and neutrons.
The neutron-proton hypothesis is consistent with the phenomena of radioactivity. Since there are several there reasons why electrons can not be present in the nucleus, it must be concluded that in β-radioactivity, the electron is created in the act of emission. i.e. as a result of a change of a neutron within the nucleus into a proton, an electron, and a new particle called neutrino.
Exchange of mesons.
In free state they are unstable:
P n ve meson (e+)
n P ve meson (e-)
An α particle can be formed by the combination of two protons and two neutrons. electrons.

9. Note:
The neutron is not regarded as a composite system formed by a proton and an electron. The neutron is a fundamental particle in the same sense that the proton is. The two are sometimes called nucleons in order to indicate their function as the building blocks of nuclei.

10. Additional properties of atomic nuclei The first property is the statistics to which nuclei are subjected
The properties of protons, neutrons, and electrons (atomic nuclei) cannot be described on the basis of classical statistics, so, two new forms of statistics have been devised, based on quantum mechanics rather than on classical mechanics.
There are the Bose-Einstein statistics.
And Fermi-Dirac statistics.
A nucleon is described by a function of its 3 space coordinates and the value of its spin. (1/2ћ or -1/2ћ)
The Fermi- Dirac statistics apply to systems of particles for which the wave function of the systems is anti symmetrical
I.e. It (changes sign when all of the coordinates of two identical particles are interchanged).
It has been deduced from experiments that:
All nuclei of odd mass no. (A) → obeys the Fermi-Dirac statistics.
And all nuclei of even mass no. → obey the Bose-Einstein statistics.

11. The second property is the parity
A good approximation, the wave function of a nucleus may be expressed as the product of a function of the space coordinates and a function depending only on the spin orientation.
 The motion of the nucleus is said to have even parity if its wave function is unchanged when the space coordinates (x, y, z) are replaced by (-x, -y, -z). I.e. when the nucleus position is reflected about the origin of the x, y, z system of axis. The motion of the nucleus is said to have odd parity if the of its wave function is changed when the space coordinates (x, y, z) are replaced by (-x, -y, -z)

12. Radiation
Radiation: The process of emitting energy in the form of waves or particles.
Where does radiation come from?
Radiation is generally produced when particles interact or decay. A large contribution of the radiation on earth is from the sun (solar) or from radioactive isotopes of the elements .
Radiation is going through you at this very moment!

13. Radioactivity
By the end of the 1800s, it was known that certain isotopes emit penetrating rays. Three types of radiation were known:
Alpha particles (a)
Beta particles (b)
Gamma-rays (g)

14. Where do these particles come from ?
These particles generally come from the nuclei of atomic isotopes which are not stable.
The decay chain of Uranium produces all three of these forms of radiation.
Let’s look at them in more detail…

15. Note: This is the mass number, which is the number of protons plus neutrons
Alpha Particles (a)
Radium
R226
Radon
Rn222 + p n n p
a (4He)
88 protons
138 neutrons
86 protons
136 neutrons
2 protons
2 neutrons
Note: The 226 refers to the atomic weight, which is the equal to the number of protons plus neutrons
alpha-particle (a) is a Helium nucleus. It’s the same as the element Helium, with the electrons stripped off !

16. Yes, the same neutrino we saw previously
Beta Particles (b)
Carbon
C14
Nitrogen
N14 + e-
6 protons
8 neutrons
7 protons
7 neutrons
electron
(beta-particle)
We see that one of the neutrons from the C14 nucleus “converted” into a proton, and an electron was ejected. The remaining nucleus contains 7p and 7n, which is a nitrogen nucleus. In symbolic notation, the following process occurred:
n  p + e ( + n)
Note that in beta decay, the atomic mass not change, since the neutron and proton have nearly the same mass…
Yes, the same neutrino we saw previously

17. 10 neutrons (in excited state) 10 neutrons (lowest energy state)
Gamma particles (g)
In much the same way that electrons in atoms can be in an excited state, so can a nucleus.
Neon
Ne20
Neon
Ne20 +
10 protons
10 neutrons (in excited state)
10 protons
10 neutrons (lowest energy state)
gamma
A gamma is a high energy light particle.
It is NOT visible by your naked eye because it is not in the visible part of the EM spectrum.

18. Gamma Rays Neon Ne20 Neon Ne20 +
The gamma from nuclear decay is in the X-ray/ Gamma ray part of the EM spectrum (very energetic!)

19. Natural radioactivity
It was found that, the product of radioactive decay is it self radioactive.
Radioactive A
Parent λ1
Radioactive B
Daughter 
B behaves chemically in a different
manner to A and C.
Radioactive C

20. How do these particles differ ?
Mass* (MeV/c2)
Charge
Gamma (g)
Beta (b)
~0.5 -1
Alpha (a)
~3752 +2
* m = E / c2

21. Types of Ionizing Radiation
Alpha Particles
Stopped by a sheet of paper
Radiation
Source
hazard
Beta Particles
Stopped by a layer of clothing
or less than an inch of a substance
(e.g. plastic)
5. Types of Ionizing Radiation
Alpha particles. Alpha particles are ejected from (thrown out of) the nuclei of some very heavy radioactive atoms (atomic number > 83). An alpha particle is composed of two neutrons and two protons. Alpha particles do not penetrate the dead layer of skin and can be stopped by a thin layer of paper or clothing. If an alpha-emitting radioactive material gets inside the body through inhalation, ingestion, or a wound, the emitted alpha particles can cause ionization that results in damage to tissue. It is less likely that a patient would be contaminated with an alpha emitter.
Beta particles. A beta particle is an electron ejected from the nucleus of a radioactive atom. Depending on its energy, beta radiation can travel from inches to many feet in air and is only moderately penetrating in other materials. Some beta radiation can penetrate human skin to the layer where new skin cells are produced. If high-enough quantities of beta-emitting contaminants are allowed to remain on the skin for a prolonged period of time, they may cause skin injury. Beta emitting-contaminants may be harmful if deposited internally. Protective clothing (e.g., universal precautions) typically provides sufficient protection against most external beta radiation.
Gamma rays and x rays (photons). Gamma rays and x rays are able to travel many feet in air and many inches in human tissue. They readily penetrate most materials and are sometimes called “penetrating” radiation. Thick layers of dense materials are needed to shield against gamma radiation. Protective clothing provides little shielding from gamma and x radiation, but will prevent contamination of the skin with the gamma-emitting radioactive material. Gamma and x radiation frequently accompany the emission of beta and alpha radiation.
Gamma Rays
Stopped by inches to feet of concrete
or less than an inch of lead

22. Radiation Types - Alpha
An alpha particle consists of two protons and two neutrons
Very large on an atomic scale
Positively charged
Penetration in materials
Outside the body, an alpha emitter is not a hazard unless it is on the skin
Inside the body, an alpha emitter is a bigger hazard if it deposits its energy in sensitive tissue

23. Radiation Types - Alpha
Common alpha-particle emitters
Radon-222 gas in the environment
Uranium-234 and -238) in the environment
Polonium-210 in tobacco
Common alpha-particle emitter uses
Smoke detectors
Cigarettes/cigars
Static eliminators

24. Radiation Types - Beta A beta particle is a charged electron
Has the size and weight of an electron
Can be positively or negatively charged
Penetration in materials
At low energies, a beta particle is not very penetrating – stopped by the outer layer of skin or a piece of paper
At higher energies, a beta particle may penetrate to the live layer of skin and may need 0.5” of plexiglass to be stopped

25. Radiation Types - Beta Penetration in materials, continued
Inside the body, a beta particle is not as hazardous as an alpha particle because it is not as big
Because it is not as big, it travels farther, interacting with more tissue (but each small piece of tissue gets less energy deposited)

26. Radiation Types - Beta Common beta-particle emitters
Tritium (hydrogen-3) in the environment
Carbon (14) in the environment
Phosphorus (32) used in research and medicine
Common beta-particle emitter uses
Carbon dating
Basic research
Cancer treatment

27. Radiation Types - Photon
A photon is an x or gamma ray
Has no weight
Has no charge
Penetration in materials
At low energies, a photon can be stopped by a very thin (almost flexible) layer of lead or several centimeters of tissue
At higher energies, inches of lead might be necessary to stop a photon and they can pass right through a human

28. Radiation Types - Photon
Common photon emitters
Cesium (137)
Technetium (99m) used in medicine
Iodine (131) used in medicine
Common photon emitter uses
Determining the density of soil
Diagnosing disease
Cancer treatment

29. Photon Decay 99mTc 99Tc Stable Nucleus Excited Nucleus Gamma ray
Gamma emissions occur during transitions such as fission, radioactive disintegration and electron-positron annihilation.
Gamma rays are monoenergetic electromagnetic radiations that are emitted from nuclei of excited atoms following radioactive transformation; they provide a mechanism for ridding excited nuclei of their excitation energy.
Source: Cember, H, Introduction to Health Physics, 1989
Stable Nucleus
Excited Nucleus