Optional Unit VIII: Atomic Physics
A. Atomic Theory

Key Concepts

Rutherford's gold foil experiment, performed in conjunction with Geiger and Marsden, provided evidence for the nucleus due to the scattering of alpha particles. The repulsion of some alpha particles suggested that the nucleus is positively charged, containing protons .

within the nucleus of the atom.

The atomic number describes the number of protons in the nucleus. For a neutral atom this is also the number of electrons outside the nucleus.

Subtracting the atomic number from the atomic mass number gives the number of neutrons in the nucleus.

Isotopes are atoms of the same element (i.e., they have the same number of protons, or the same atomic number) which have a different number of neutrons in the nucleus. Isotopes of an element have similar chemical properties.

Radioactive isotopes are called radioisotopes.

Most of the elements in the periodic table have several isotopes, found in varying proportions for any given element.

The average atomic mass of an element takes into account the relative proportions of its isotopes found in nature.

A nuclear binding force holds the nucleus of the atom together. The nuclear mass defect, a slightly lower mass of the nucleus compared to the sum of the masses of its constituent matter, is due to the nuclear binding energy holding the nucleus together.

The mass defect can be used to calculate the nuclear binding energy, with E = mc².

The average binding energy per nucleon is a measure of nuclear stability. The higher the average binding energy, the more stable the nucleus.

The Bohr model of the atom described the electrons as orbiting in discrete, precisely defined circular orbits. Electrons can only occupy certain allowed orbitals. For an electron to occupy an allowed orbit, a certain amount of energy must be available.

Each orbit is assigned a quantum number, with the lowest quantum numbers being assigned to those orbitals closest to the nucleus. Only a specified maximum number of electrons can occupy an orbital. Under normal circumstances, electrons occupy the lowest energy level orbitals closest to the nucleus. By absorbing additional energy, electrons can be promoted to higher orbitals, and release that energy when they return back to lower energy levels.

The Bohr model of the atom helped to offer one possible explanation for the emission spectrum formed by hydrogen and other gases.

Photons are used to describe the wave-particle duality of light. The energy of a photon depends upon its frequency. This helps to explain the photoelectric effect; only photons having a sufficiently high energy are capable of dislodging an electron from the illuminated surface.

E = hv where E is the photon energy in J, v is the photon frequency in Hz, and h is Planck's constant, 6.626 x 10^-34 J/Hz.

Quantum theory offers a mathematical model to help explain the nature of the atom.

Quantum theory describes a region surrounding the nucleus which has the highest probability of locating an electron. These orbital "clouds" have some unusual and interesting shapes.

Learning Outcomes

Students will increase their abilities to:

1. Define the following terms: atomic number, isotope, radioisotopes, nuclear binding force, average binding energy, nuclear mass defect, nuclear binding energy, photon.

2. Use the atomic number of an element to determine the number of protons in a nucleus.

3. Infer the number of electrons in a neutral atom from the atomic number of an element.

4. Use the atomic mass number and the atomic number to determine the number of neutrons in the nucleus of an atom.

5. Recognize that isotopes of an element have similar chemical properties, but different physical properties.

6. Give an example of an element which contains isotopes and show how those isotopes differ from each another.

7. Explain that the average atomic mass of an element takes into account the relative proportions of its isotopes found in nature.

8. Explain some of the important characteristics of the Bohr model of the atom.

9. Identify, interpret, or explain the use of quantum numbers in orbital theory.

10. Show how the Bohr model of the atom offered explanations for some physical phenomena, while failing to provide a suitable explanation for others .

11. Explain how photons are used to describe the wave-particle duality of light.

12. Explain that quantum theory helps to explain the photoelectric effect, the Compton effect, and other important physical principles which earlier theories did not account for adequately.

13. State that quantum theory describes a region surrounding the nucleus which has the highest probability of locating an electron.

14. Describe some of the electron orbital descriptions provided by quantum theory.

Teaching Suggestions, Activities and Demonstrations

Caution: It is recommended that no experimentation be done with radioactive sources. Use simulations, computer generated models, or audiovisual aids instead. Very low level sources ofionizing radiation can be used if other simulations are not appropriate, but extreme care should always be exercised. It is also important to label radioactive sources properly and to store them in a safe, secure location.

1. Using a gas discharge tube or a cathode ray tube, connected to a high voltage power supply, demonstrate what happens to the beam if it allowed to interact with: a) light striking the beam at right angles, b) an object carrying a static charge, and c) a magnetic field.

   Caution: Special care should be taken when using a high voltage power supply. Also, gas discharge tubes may produce dangerous x-rays. Teachers should demonstrate this, observing appropriate safety precautions. Roentgen's accidental discovery of x-rays can be simulated by placing a fluorescent object near the gas discharge tube. An unexposed sheet of 4 inch by 5 inch type 57 polaroid film (ISO 3 000) placed in the vicinity for a prolonged period of time will also demonstrate this.

2. Prepare 30 small cubes painted green on all sides and another 30 cubes with five blue sides and one red side. The 30 blue-red faces simulate radioactive nuclides after decay. Shake the red-blue cubes and allow them to scatter on a flat surface. Any red sides facing up represent nuclides that have undergone decay. Count the number of red sides facing up after each trial. Record the results. Replace the cubes that have the red face up with a green cube (representing a stable daughter nucleus) and continue shaking and scattering several more times. On each shake the total number of cubes being shaken should be 30.

   Record all observations. Generate a nuclear decay curve, plotting the number of blue faces against the number of shakes. From the results, determine the half-life of the sample.

   Is there a statistical model to predict the half-life? What effect does the sample size have on the decay curve and the half-life? (i.e., Start with 20 red-blue cubes instead of the 30 used in the first trial. Repeat the test.)

   (To obtain statistically significant results, use more than 30 cubes.)

3. Research the biological effects of ionizing radiation. This activity can be done in conjunction with Biology 30.

4. Develop a report on the solar wind, the results of solar flare activity, the aurora borealis, or some other phenomenon related to cosmic rays.

5. The photoelectric effect and the Compton effect helped to give rise to quantum theory. Research these two phenomena. Attempt to explain why theories which were prevalent at the time failed to account for these phenomena.

6. If a group of students who have some experience in programming are interested, they can develop a computer program to simulate radioactive decay.