SAT Physics Nuclear Reactions - Nucleons

SAT Physics Nuclear Reactions - Nucleons

NUCLEONS
Nuclear reactions are concerned with the nucleus of the atom and the particles it contains. The subatomic particles contained in the nucleus of an atom are known as nucleons. They consist of protons and neutrons. Both the mass and the number of these particles are important when analyzing nuclear reactions.

Atomic Mass Units
A specialized unit of mass known as the atomic mass units (u) was devised to make working with the mass, of fundamental particles easier. The mass of both the proton and neutron were originally thought to be the same. They were each assigned a mass of 1.0 atomic mass unit for simplicity. It has since been determined that the masses are very similar but that the neutron has a slightly greater mass. The modern definition of an atomic mass unit is 1-1 the mass of a carbon-12 atom. By using this scale, a proton has a mass of 1.00728 atomic mass units while a neutron has a mass of 1.00866 atomic mass units. For rough calculations these masses are still both rounded off to 1.0 atomic mass unit. Atomic mass units are a more convenient scale to measure mass when working with fundamental particles.

Atomic Number and Mass Number
When the symbol for an element is used in a nuclear reaction, the atomic number and the mass number are written as subscripts and superscripts preceding the element’s symbol, as shown in Figure 21.1.
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Figure 21.1. Atomic number and mass number

   The atomic number is the number of protons in an atom. The number of protons defines an element. For example, all carbon atoms have 6 protons, so the atomic number of all carbon atoms is always 6. If a carbon atom gains or loses protons, it is no longer a carbon atom. Changing the number of protons causes a transmutation of the atom into a completely different type of element.
   The mass number provides three different and important numerical values.
  1. The mass number is the number of protons plus neutrons. In Figure 21.1, the mass number is 12. So there are 12 protons and neutrons in a carbon-12 atom. Since the atomic number is the number of protons only, the number of neutrons can be deduced by subtracting the atomic number from the mass number. The carbon atom in Figure 21.1 has 6 neutrons (12 - 6 = 6).
  2. The mass number is also the atomic mass (mass of a single atom) measured in atomic mass units. The carbon atom in Figure 21.1 has a mass of 12 atomic mass units.
  3. In addition, the mass number is also the molar mass (mass of one mole of atoms) measured in grams per mole. This is widely used in chemistry but is not a factor in this chapter.
SUBATOMIC PARTICLES
Table 21.1 lists the fundamental particles most likely to be encountered in nuclear reactions. Knowing the mass and atomic number of these basic particles will be an asset when analyzing nuclear reactions. In addition, the charged particles will interact with electric and magnetic fields. You must know which particles are charged and whether that charge is positive or negative. Occasionally, questions ask how these particles move in electric and magnetic fields. Although you do not need to know the exact mass of the particles listed in the table, you should be able to list them in order of their masses.

Table 21.1 Subatomic Particles
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In addition to protons, neutrons, and electrons, three new and important subatomic particles plus gamma radiation have been listed in the table.

Neutrino
Neutrinos are often a product of radioactive decay and nuclear reactions. A neutrino, ve, is a neutral particle with very little (nearly zero) mass. Neutrinos are more common in the universe than electrons and protons. However, neutrinos do not interact well with matter, and they have insignificant mass. Neutrinos also have an antiparticle variant known as the antineutrino, ve. Therefore, neutrinos and antineutrinos can be ignored in the types of problems seen in beginning physics courses. They have been included here as their symbols may be encountered in nuclear reaction formulas.

Alpha Particle
An alpha particle is simply the nucleus of a helium atom without any electrons. The alpha particle has a mass number of 4. This means it contains 4 nucleons (protons + neutrons), and it has a mass of 4.0 atomic mass units. Of the particles listed in Table 21.1, the alpha particle is the most massive. The atomic number is 2, indicating that the alpha particle contains 2 protons. As a result, the alpha particle must also contain 2 neutrons. Since the alpha particle contains two protons and no electrons, it is positively charged. The charge of an alpha particle is equal to the charge of two protons (+3.2 X 10-19 coulombs). As a result, it interacts with electric and magnetic fields as would any positive charge.

Beta Particle
A beta particle is an electron produced when a neutron undergoes a transmutation to become a proton. Neutrons are actually protons and electrons that have combined into a single particle. In the process, the positive and negative charges cancel and the neutron becomes slightly more massive than the proton. Under the right conditions, a neutron may spontaneously divide and become a proton and an electron. Under the right conditions, a neutron may spontaneously divide and become a proton and an electron (plus an antineutrino, 1-4 which can be ignored).
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When this happens, the electron originates in the nucleus and not in the energy levels surrounding the nucleus, where ordinary electrons are found. This electron, known as a beta particle, is ejected from the atom with high energy.
Electrons and beta particles have too little mass to affect the atomic mass of an atom noticeably. Think of electrons as adding as much mass to an atom as eyelashes add to the mass of a person. The mass of electrons is therefore not included in the atomic mass. The mass number for an electron has a value of 0 as expected. However, the atomic number (number of protons) is shown as -1. Essentially, an electron is the negative of a proton. If this is the case, shouldn’t all stable atoms have an atomic number of 0 since the protons and electrons cancel each other? The atomic number is used for nuclear reactions and for particles that are inside the nucleus. Electrons in the energy levels surrounding the nucleus are not inside the nucleus and their atomic number is ignored. However, when electrons such as beta particles engage in nuclear reactions, their atomic number (-1) is important to balance the particles during the reaction. The electrical charge of a beta particle is the same as that of any electron (-1.6 x 10-19 coulombs). A beta particle interacts with electric and magnetic fields in the same manner as does an electron.

Gamma Ray (Gamma Radiation)
Just like electrons, protons and neutrons can move between energy levels within the nucleus. Nuclear reactions can excite nucleons to higher energy levels. When the nucleons subsequently drop to lower energy levels, they emit photons. The photons emitted when nucleons drop to lower energy levels are incredibly energetic compared to those emitted when orbiting electrons change energy levels. These energetic photons are known as gamma rays, γ. Gamma rays are a form of electromagnetic radiation. They do not have mass or charge, and they are not influenced by electric or magnetic fields.

ISOTOPES
Although an atom must have a specific number of protons (a set atomic number) to remain a specific element, an atom does not need to contain a definite number of neutrons. Each element may have several combinations of neutrons that allow atoms of that element to
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number of carbon is set, the mass number may vary. The forms of carbon with different numbers of neutrons are the possible isotopes of the carbon atom. Isotopes are the same chemical element but have different numbers of neutrons. The isotopes of an element are often reported with the element name followed by the mass number (carbon-12, carbon-13, and carbon-14). There is no need to report the atomic number (6) since it is a known fact that all carbon atoms have six protons.
Isotopes vary in both mass and their atomic stability. The difference in mass between isotopes is obvious. Carbon-14 has a mass of 14 atomic mass units, while carbon-12 has a mass of 12 atomic mass units. The mass is important in balancing nuclear reactions and when calculating the energy involved in nuclear reactions. However, the instability of certain isotopes, such as carbon-14 and uranium-235, allow nuclear reactions to occur.

THE STRONG FORCE
Students rarely ask why the protons in the nucleus cluster together when they should repel each other due to electrostatic forces. As it turns out, another force is operating in the nucleus, the strong force. The strong force attracts nucleons to one another. It attracts protons to protons, neutrons to neutrons, and protons to neutrons. While the electrostatic force is trying to separate the protons, the strong force holds them together. The magnitude of the strong force is greater than that of the electrostatic force. However, the strong force operates only at very small distances, such as those inside the nucleus. If a proton in the nucleus is moved away from the center of the atom, the strong force weakens with increasing distance. At a certain distance, the repulsion due to the electrostatic force will exceed the strong force. When this occurs, the electrostatic force will accelerate the proton out of the atom.
    Adding neutrons to the nucleus helps hold the nucleus together. The neutrons add to the strong force, helping to hold the repelling protons near each other. In addition, the neutrons have no charge. So they do not contribute to the electrostatic repulsive force that acts to tear apart the nucleus. However, every atom has an optimum mix of protons and neutrons. When the number of protons and neutrons falls outside of an optimum range, the geometry of the nucleus weakens the strong force. This allows the electrostatic force either to eject a small portion of the nucleus or to tear apart the entire nucleus. Carbon-14 and uranium-235 are classic examples of unstable nuclei. When these atoms undergo nuclear reactions their nuclei experience changes in compositions. As a result, these elements undergo a transmutation into entirely new elements.

MASS-ENERGY EQUIVALENCE
During a nuclear reaction, the mass of the reactants at the start of the reaction does not equal the mass of the products produced by the reaction. The difference in mass between the products and the reactants is known as the mass defect, Am. The mass defect is associated with the energy involved in a nuclear reaction. The amount of energy, E, associated with the mass defect can be calculated using the speed of light in a vacuum, c, and Albert Einstein’s famous equation:
E= (Δ m)c²
   This equation demonstrates mass-energy equivalence. Under certain conditions, such as nuclear reactions, matter may be converted into energy or energy may be converted into matter.
Nuclear reactions release energy by converting a small amount of the original mass into energy. In nuclear reactions where energy is released, the reactants (ingredients) have more mass than the products formed during the reaction. To balance and account for all the original mass during the reaction, the mass defect must be added to the product side of the reaction.
Reactants → Products + Δm
   For example, a neutron splitting to form a proton and an electron can be shown as follows.
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   When the symbol for each particle is replaced by the appropriate mass in atomic mass units, then it becomes apparent that the product side of the reaction is missing mass. The symbol for the mass defect is added to the side with the least amount of mass. So the magnitude of the mass defect can be calculated.
The mass defect, Am, is the small amount of mass that is converted into energy, E= (Δm)c2, during the reaction! The actual calculation involves values and conversions that would be difficult to complete without a calculator, and is unlikely to be tested. The values are shown here to assist you in understanding the concept of converting matter into energy.
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   This amount of energy is released when a neutron becomes a proton and an electron. Energy is a product of this reaction, and the mass defect can be replaced with energy in the reaction equation.
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   Note that reactions can also run in reverse. If the above example were reversed, combining a proton and an electron would create a neutron. In the reverse reaction, the reactants would have less mass, so the mass defect would be added to the left side of the equation. In this process, energy is a reactant and energy must be converted into matter to allow the reaction to progress.

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