What are CPM? What are the three types of radiation studied in this lab? Why doe
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Question
What are CPM? What are the three types of radiation studied in this lab? Why does radioactivity seem to be more common for heavier elements? What is the inverse square law for radiation? Explain in your own words what it means. Write the absorption law for radiation. Define the variables. Explain in your own words what it means. Define the term "half-life". Almost all of the atoms with which we come into daily contact have stable nuclei. Given that there are many more unstable isotopes than stable ones, how could this state of affairs have arisen? A certain Geiger counter reads 40,000 cpm. What is the error on this number?Explanation / Answer
CPM
Types
Three types of radiation - Alpha, Beta, Gamma
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.
The Inverse Square Law
The Absorption Law
Analysis
Radioactive Decay and Half-life
The Inverse Square Law
The Absorption Law
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