PHY 102

1. PHY 102 NUCLEAR PHYSICS

2. ATOMIC NUCLEUS • Rutherford’s Experiment • Energetic alpha-particles scattered on thin gold foil • Most alpha-particles scattered through small angles • Few alpha-particles scattered through large angles (back-scatter)

3. ATOMIC NUCLEUS • Back-scattering can only be explained by the alpha-particle encountering a massive positive charge • Most alpha-particles experiencing forward-scatter implies the size of the nucleus is small compared to the size of the atom

4. ATOMIC NUCLEUS • To estimate the size of the nucleus, consider a head-on collision of alpha-particle with a gold nucleus • At distance of closest approach, d, alpha-particle kinetic energy is converted to Coulomb potential energy.

5. ATOMIC NUCLEUS • Terminologies: • Nuclide – a specific nucleus of interest, not the atom as a whole • Nucleon – generic name for both protons and neutrons • Atomic number – number of protons in a nuclide (Z). • Mass number – number of nucleons in a nuclide (A) • N = number of neutrons in the nuclide. • Nuclide X written as • e.g.

6. ATOMIC NUCLEUS • Isotopes – nuclides with the same atomic number but different neutron number e.g. • Isotones – nuclides with the same neutron number but different mass number • Two forces interacting between the nucleons inside the nucleus – Coulomb force, strong (nuclear) force.

7. ATOMIC NUCLEUS • Coulomb force is repulsive and has long range, operates between p-p only. • Nuclear force is attractive, has short range, operates between n-n, n-p, p-p. • The two forces compete. When they do not balance, the nuclide is unstable – emits radiation in order to become stable. • Only nuclides along stability line are stable, others are radio-active.

8. ATOMIC NUCLEUS

9. ATOMIC NUCLEUS

10. ATOMIC NUCLEUS • Isobars – nuclides with the same mass number (see isobar line in last slide). • Nuclear Radius • Calculate the radius of nucleus.

11. ATOMIC NUCLEUS • Nuclear Masses • Nuclear masses are expressed in units of “atomic mass unit” – the unit in which the mass of Carbon-12 is exactly 12u. • Often nuclear masses are given units of energy, converting mass into its energy equivalence

12. ATOMIC NUCLEUS • Converting the “atomic mass unit” to energy • Mass excess

13. ATOMIC NUCLEUS • Nuclear binding energy – the mass of a nuclide is less the sum of masses of individual nucleons making up the nuclide. • Total binding energy of the nuclide is the difference between the sum of masses of its nucleons and the nuclide mass

14. ATOMIC NUCLEUS • Binding energy per nucleon = B.E. / A • Varies from nuclide to nuclide, maximum around Iron-56

15. ATOMIC NUCLEUS

16. RADIOACTIVE DECAY • An unstable nucleus transmutes to another nucleus by emitting a particle, or to a lower energy level of the same nucleus by emitting a gamma ray. • If we have a gram of radioactive material of the same element (no. of nuclei present ), we cannot predict which nucleus will transmute at a particular time. • Radioactive decay is statistical.

17. RADIOACTIVE DECAY • If there are N radioactive nuclei in a sample at some time t, the number that will decay is proportional N and the time interval, . • Negative sign because decay implies decrease in N at time goes on.

18. RADIOACTIVE DECAY • We can write for • Integrating and assuming the number of nuclei at is we obtain a time dependence • is called the decay constant – unit is per sec or per hour or per year depending on the unit of time.

19. RADIOACTIVE DECAY • Half life of a radioactive element is the time that will lapse before half of the initial nuclei have decayed, • We can show that • Activity, R, is defined as the decay rate

20. RADIOACTIVE DECAY • Activity, R, is • where is the activity at time . • Unit of activity is becquerel • Older unit = curie

21. RADIOACTIVE DECAY • A fresh sample of KCl of mass 2.71 g is found to be radioactive due to the presence of K-40. The decay rate was found to be 44.90 Bq. If the relative abundance of in the sample is 0.0117%, calculate the half-life of this radionuclide. • Molar mass of K = 39.102 g/mole, molar mass for chlorine = 35.453 g/mole • Mass of 1 mole of KCl = 74.555 g

22. RADIOACTIVE DECAY

23. ALPHA PARTICLE EMISSION • When a radionuclide emits an alpha particle, it transmute into another nuclide e.g. • The energy of disintegration, Q, determines either this emission can occur spontaneously or not. If the emission can occur spontaneously. If , emission cannot occur spontaneously. • = sum of initial and final nuclide masses.

24. ALPHA PARTICLE EMISSION

25. ALPHA PARTICLE EMISSION • Calculate the disintegration energy for the proton decay of . • Since disintegration energy is negative, emission cannot proceed spontaneously.

26. BETA DECAY • A radionuclide can decay by emitting an electron or a positron. Beta emission occurs spontaneously and is also a statistical process. Examples of beta decay: • are neutrino and anti-neutrino. Both particles are electrically neutral and have negligible masses • In decay, a neutron inside the nucleus is converted to a proton and an electron and an anti-neutrino.

27. BETA DECAY • In decay, a proton inside the nucleus is converted to a proton, a positron and a neutrino. • The probability of a neutrino or anti-neutrino interacting with any other particle is very very low. The reason for suspecting its existence before it was detected is because of the continuous energy spectrum of the electron or positron emitted, instead of having a definite energy. • There is a maximum energy that an electron or a positron emitted from a particular nucleus can have.

28. BETA DECAY

29. BETA DECAY • The energy of disintegration, Q, equals the maximum kinetic energy that the electron or positron can have. • Calculate the disintegration energy for the beta decay of Atomic mass of . Atomic mass of • Note the masses given are atomic masses i.e. include the masses of the electrons in the atom. In alpha and decays the electron masses cancel out.

30. BETA DECAY • Calculation for is different.

31. MEASURING RADIATION DOSAGE • The effect of radiation on human beings is of concern since ionizing radiation affects human health • Absorbed Dose: a measure of the radiation dose (energy / unit mass) actually absorbed by a specific object e.g. human hand, chest, etc. Unit of absorbed dose is the Gray. Older unit is the rad. • Average absorbed dose per annum for non-radiation workers is about 2 mGy

32. MEASURING RADIATION DOSAGE • Dose equivalent: though different types of radiation (alpha, beta, neutrons, etc.) may deposit the same amount of energy in an organ, the biological effects are different. The biological effects of a dose from different radiations are obtained by multiplying the dose by a number – radiation biological effect (RBE).

33. MEASURING RADIATION DOSAGE • Units of dose equivalent is sievert (Sv) or rem. • Non-occupationally exposed person should not receive more than whole-body dose equivalent of 5 mSv in any one year. • The dosage comes from – medical diagnosis, environmental radiation, cosmogenic radiation.

34. MODELS OF THE NUCLEUS • Collective model • Nucleons move at random within nuclear volume • Nucleons interact strongly with one another like molecules in a drop of water • Model able to explain nuclear masses, binding energies, many nuclear reactions especially nuclear fission. • Independent Particle model • Each nucleon moves independently under the potential created by other nucleons • Each nucleon moves in a well-defined quantum orbit

35. MODELS OF THE NUCLEUS • Independent Particle model • Nucleons obey Pauli exclusion principle – no two nucleons occupy the same quantum state. • Nucleon arrangement in the nucleus demonstrates closed shell as in the case of the atom. • The numbers of nucleons that form closed shells in the nuclear case are 2, 8 , 20, 28, 50, 82, 126 • These numbers are referred to as magic numbers. • Nuclei having Z or N magic number is found to be very stable. Most especially doubly-magic number nuclei e.g.