Radioactivity


SPECIFIC OBJECTIVES

To be able to distinguish the three types of radiation; to understand the way in which the intensity of radiation changes with

EQUIPMENT

Geiger counters; alpha, beta, and gamma radioactive sources; cardboard, aluminum, and lead sheets; dice.

BACKGROUND

The atom is composed of a small heavy nucleus, containing protons and neutrons, surrounded by light electrons. The protons are positively charged; the neutrons are neutral; and the electrons are negatively charged. In electrically neutral atoms, the number of protons in the nucleus is the same as the number of electrons. Since the electrons determine all the chemical properties of the substance, and since the number of electrons is determined by the number of protons, every substance with unique chemical characteristics (element) is distinguished by the number of protons. Changing the number of protons in the nucleus is equivalent to changing the element.

The nucleus is positively charged since the protons have positive electric charge and the neutrons are neutral. Why don't the protons repel each other and fly apart? The neutrons bind the protons together with the strong nuclear force, which is stronger than the Coulomb electrical repulsion, at least for the smaller nuclei. Most of the lighter elements have an equal number of protons and neutrons, but many of the heavier elements tend to have more neutrons than protons. For example, the most common form of uranium has 92 protons and 146 neutrons. Eventually, the neutrons are not able to supply enough nuclear "glue" to keep larger numbers of protons from flying apart.

Atoms with the same number of protons but different numbers of neutrons are called isotopes. There are many more unstable isotopes than stable ones.

More than 99.999% of the atomic nuclei in objects around you are stable, that is, they do not decay. Some nuclei, however, are unstable. The process of spontaneous change, and the associated emission of energetic particles, is called radioactivity, or radioactive decay.

The three types of radiation that we will study are:

In alpha decay, the unstable nucleus throws off a chunk of itself. Since the chunk contains two protons, the decay product is a different element.

In beta decay, one of the nuclear neutrons is converted into a proton, an electron, and another particle called a neutrino which is extremely difficult to detect. The proton remains in the nucleus and the electron is ejected as a beta ray. Since the number of protons has increased, the decay product is a new element.

In gamma decay, the unstable nucleus shifts from a high energy state to a lower energy state. The difference in energy is carried away by a photon, the same particles that make up visible light. The nuclear energy shifts are so large, however, that the photons are much more energetic than visible light or even X-rays. Since the number of protons in the nucleus has not changed, the decay product is the same element, but in a more stable form.

Radioactive Decay and Half-life

Similar to a batch of popcorn, it is impossible to determine when a particular radiaoactive atom will decay. What can be measured is how long it takes on average for one half of a large sample of atoms to decay. The term half-life describes this length of time; it may be measured in any unit of time from seconds to years. For example, a radioactive sample with a half-life of 20 minutes contains 1,000,000 atoms at time zero. After 20 minutes, 500,000 (on average) will remain. After an additional 20 minutes, 250,000 (on average) will remain, and so on.

The radioactive decay law is

I(t) = Io 2^(-t / T½ )

where Io is the intensity of the radiation at time zero, I(t) is the intensity of the radiation after time t, and T½ is the half-life of the sample.

The Inverse Square Law

In the absence of absorption (see below), the alpha, beta, and gamma rays resulting from the decay of a sample of unstable nuclei speed away from the sample uniformly in all directions. Imagine two mathematical spheres with the sample at the center of both spheres and one sphere having twice the radius of the other. All the particles that penetrate the inner sphere will also penetrate the outer sphere (because none are absorbed). However, the number of particles per square centimeter at the outer sphere will be lower because the particles spread out. In fact, the intensity will be lower by the ratio of the area of the two spheres. The inverse square law for radiation is a result of geometry in three dimensions. The intensity is inversely proportional to distance squared from the source:

I = A / d2


where I is the intensity of the radiation, A is a proportionality constant, and d is the distance from the source.

The Absorption Law

Nuclear radiation is absorbed by various materials at different rates. However, it has been determined experimentally that all radiation is absorbed by all materials in a similar manner. The absorption law is

I(x) = Io 2^(-x / D½ )


where Io is the intensity of the radiation falling on the material, I(x) is the intensity of the radiation transmitted through thickness x of the absorbing material, and D½ is the half-thickness of the material. The half-thickness of a material is defined to be the amount of material which will absorb one half of the incident radiation.

The Geiger Counter

consists of a metal-coated cylindrical tube filled with an inert gas like argon and a wire running through its center. The tube and wire are held at a large potential difference (roughly 1000 volts). Normally, the potential difference is not enough for a spark to jump from the wire to the metal wall of the tube. However, when an alpha, beta, or gamma ray passes through the tube, the radiation ionizes the gas in the tube creating free electrons, and a spark jumps easily through the ionized gas. When a voltage pulse is detected, the Geiger counter gives an audible "click" (familiar from very bad 1950's science fiction movies). The counter also has a needle scale for measuring large rates of clicks, too fast for humans to count.

The Geiger counter measures the intensity (I) of radiation in units called CPM for "counts per minute".

Cosmic Ray Background

The Earth is constantly bombarded by cosmic rays (mostly very high energy protons) with origins outside the Solar System. When the cosmic rays encounter the Earth's atmosphere they create "showers" of secondary particles, some of which reach the Earth's surface. One secondary particle with a large penetrating power is the muon which can travel through several feet of concrete and steel. Since the basement laboratory is not an effective shield against these particles, we account for this cosmic ray background by counting the average number of particles that pass through the Geiger tube when no radioactive sources are present. When sources are present, the background count is subtracted from the measurement. The difference is the number of particles coming solely from the radioactive source.

PROCEDURE

Radioactive Decay and Half-life

Radioactive sources that are safe to handle generally have long half-lives. For example, uranium-238 has a half-life of 4.5 billion years. The exponential decay in the number of counts per minute would not be observable in the three-hour lab period. Sources with a half-life of a few minutes can be observed in the lab period, but are very dangerous to handle. For this reason, we use a model of radioactive decay.
  1. Count the total number of dice in the container.

  2. If the dice represent radioactive atoms about to decay, then after one half-life one half of the atoms will remain. After two half-lives one quarter of the initial number will remain. Plot the theoretical number of atoms which have not yet decayed versus the number of half-lives.

  3. Spill the dice on the table. Remove all the dice showing even numbers from the experiment (they represent atoms that have decayed).

  4. Count and record the number of odd dice, put them back in the container, randomize, and spill these dice on the table.

  5. Repeat until all the dice are gone (until all the atoms have decayed).

  6. Plot the experimental points on the same graph as the theoretical curve. Notice the statistical fluctuations from theory.

The Inverse Square Law

  1. Plug in and turn on the larger Geiger counter with the vertical scale.

  2. Depress and hold the red button to read the tube voltage. Set the tube voltage to the value marked on the counter. This may require periodic adjustment during the experiment.

  3. Set the range selector to the scale that is most appropriate for your measurement, that is, the scale with the lowest fractional error. Re-read Lab 0 to refresh your memory.

  4. Set the response control to slow. The Geiger counter can average the number of counts over a short time for quick but imprecise readings; the needle will jump about with statistical fluctuations in the CPM. We will use the slow response setting which requires a longer period for the counter to average the data, but the final reading will be more precise; the needle will not bounce erratically.

  5. Remove any sources from the immediate vicinity of the Geiger counter. Take a background count by ear for three minutes. Divide by three to get an average background CPM. This value must be subtracted from all measurements taken with this meter.

  6. Place the beta source (green disk) on the vertical scale using the magnetic mount. The radioactive sample is embedded in the green disk so that radiation is emitted in a roughly cone-shaped pattern through the hole in the aluminum bracket. Thus, the green disk should be on the top side of the bracket.

  7. Align the window of the Geiger tube so that the radiation can enter the tube. The window should face upward and be centered on the vertical scale.

  8. Record the CPM at various distances. Remember to subtract the background count. If the count drops too low for an accurate meter reading, take the count by ear.

  9. Make a plot of Intensity (vertical axis) vs. 1 / distance2 (horizontal axis), taking more data where the graph appears sparse.

The Absorption Law

  1. Turn on the smaller Geiger counter.

  2. Carefully remove the red plastic window from the end of the probe.

  3. We will study the absorption of three types of radiation (alpha, beta, and gamma) by three materials (cardboard, aluminum, and lead).

  4. Remove any sources from the immediate vicinity of the Geiger counter. Take a background count by ear for three minutes. Divide by three to get an average background CPM. This value must be subtracted from all measurements taken with this meter. The background count from the previous exercise can not be used here because the two counters have different sensitivities.

  5. From the last exercise, we know that the intensity of radiation varies with distance from the source. Therefore, to study only the effect of absorbing material without distance dependence, be certain that the distance between the source and the Geiger tube does not vary. A good technique is to start with the maximum amount of material between the source and probe so that the smallest possible distance (greatest possible intensity) can be used, and then to remove sheets of the absorbing material. A little experimentation will tell you the largest interesting number of sheets.

  6. Make a plot of Intensity (vertical axis) vs. number of sheets of absorber (horizontal axis) for each case, 9 plots in all.

Analysis

    Radioactive Decay and Half-life

  1. A particular isotope has a half-life of five days. A sample is known to have contained one million atoms when it was prepared, but now only 100,000 atoms remain. How long ago was the sample prepared?

    The Inverse Square Law

  2. Your plot of I vs. 1 / d2 should be linear for large values of d (small values of 1 / d2), but it may level off for small values of d (large values of 1 / d2). Explain this behavior. Hint: Remember that the radiation is emitted through the hole in the aluminum bracket in a cone. A diagram of the cone and the Geiger tube window may help.

    The Absorption Law

  3. From your plots in the absorption experiment, determine the half-thickness of each of the three materials for each of the three types of radiation.



Don't forget your two random and two systematic error sources.



<-- Back to the Electricity and Magnetism Manual