SAT Physics Nuclear Reactions - Radioactive Decay

SAT Physics Nuclear Reactions - Radioactive Decay

Radioactive decay occurs when an unstable isotope spontaneously loses energy by emitting particles from its nucleus. The decay processes were named in their order of discovery by using the first three letters of the Greek alphabet: alpha (α), beta (β), and gamma (γ). After their initial discovery, it was determined that an alpha particle was in fact the nucleus of a helium atom 1, a beta particle was actually an electron, 2, and gamma radiation was not a particle at all. Instead, it is a high-frequency photon, 3. Elements that naturally decay are said to be radioactive. Radioactive substances have a critical imbalance between the number of protons and neutrons in the nucleus. As atoms become larger, more neutrons are needed to maintain stability. Uranium-235 has 92 protons and 143 neutrons. The three common forms of natural radioactivity—alpha, beta, and gamma radiation—are discussed below.

Alpha Decay
In an alpha decay, an alpha particle,1-2, is spontaneously ejected from the nucleus of an atom. If an alpha particle leaves the nucleus, the mass number of the atom is reduced by 4 while the atomic number is reduced by 2. Changing the atomic number causes a transmutation into a new element. The ejected alpha particle is the least dangerous form of radioactive decay. Although it is harmful if digested, an alpha particle can be stopped by both paper and skin.

The Product of an Alpha Decay
An isotope of uranium, 1-3, undergoes alpha decay. In the process, the atom becomes an isotope of thorium. Which of the following elements is the result of this transmutation?


The particle resulting from the decay leaves the nucleus and is subtracted. Subtract the mass number (4) and atomic number (2) of the alpha particle from the original nucleus.
   The resulting thorium nucleus has a mass number of 234 and an atomic number of 90. The answer is A.
   An isotope of thorium, 1-6, undergoes a transmutation into an isotope of radium, 1-7 What type of decay process caused this transmutation?


Determine the difference between the mass numbers and the atomic numbers.
   The mass number has decreased by 4, and the atomic number has decreased by 2. These are the mass number and atomic number for an alpha particle.

Beta Decay
A beta particle is released when a neutron in the nucleus of an atom decays into a proton and an electron. This electron originates in the nucleus and is known as a beta particle. Beta particles move at greater speeds than alpha particles and can be stopped with a thin sheet of metal, .such as aluminum.

The Product of Beta Decay
An isotope of uranium, 1-9 undergoes beta decay. In the process, the atom becomes an isotope of nitrogen. Which of the following is the result of this transmutation?


The particle resulting from the decay leaves the nucleus and is subtracted. Subtract the mass number (0) and atomic number (-1) of the beta particle from the original nucleus.
The resulting nitrogen nucleus has a mass number of 14 and an atomic number of 7. The answer is D.

Determining the Type of Radioactive Particle
An isotope of thorium,1-12, undergoes a transmutation into an isotope of neptunium, 1-13. What type of decay process caused this transmutation?


Determine the difference between the mass numbers and atomic numbers.
   The mass number is unchanged, and the atomic number decreased by -1. This is the mass number and atomic number for a beta particle.

Gamma Rays
Gamma rays are the result of a number of radioactive decay reactions, including alpha and beta decay. Gamma rays travel at the speed of light and have greater penetration than alpha or beta radiation. Very dense materials such as lead are needed to stop gamma rays. The release of gamma rays (high-energy photons) does not affect the atomic number or mass number of the atoms.

Decay Rate
The rate at which radioactive decay occurs is often measured in what is known as a half-life. One half-life is the time interval needed for half of a sample of radioactive atoms to decay. Carbon-14, for example, has a half-life of 5,740 years (1 half-life = 5,740 years). At the end of this time period, only half of the original sample of carbon-14 remains. The rest has undergone a transmutation into nitrogen-14. Table 21.2 shows how a sample consisting of 16 grams of carbon-14 would progress through several half-lives.

Table 21.2 Decay of Carbon-14

   Carbon-14 is created in Earth’s upper atmosphere by cosmic rays bombarding nitrogen gas atoms. Carbon-14 is absorbed by plants and animals, and it appears in these organisms at the same concentration levels found in the atmosphere. When an organism dies, it no longer absorbs carbon-14. The amount of carbon-14 in the organism will begin to beta decay into nitrogen. Measuring the levels of carbon-14 in the fossilized remains of dead organisms can help determine the time period when extinct species existed on Earth.

A 120-gram sample of iodine-131 has a half-life of 8.0 days. How much of the original sample remains after 24 days?


Divide the time interval by the length of time of one half-life to determine how many half-lives have passed.
During each half-life, the sample of iodine is halved. If 3 half-lives have passed, then the original 120-gram sample will be reduced by half 3 times.

A fission reaction is the splitting of a large atom into smaller atoms. A fusion reaction involves combining smaller atoms to make a larger atom. Both fission and fusion reactions involve the release of energy.

Fission of larger atoms into smaller ones is typically induced by the bombardment of the larger atom with free neutrons. The addition of a free neutron temporarily creates a larger, unstable nucleus. The attractive strong force is no longer able to hold the protons together. The repulsive electrostatic force tears apart the nucleus, forming two smaller nuclei. This process also releases several additional free neutrons and energy in the form of gamma rays. A common fission reaction occurring in nuclear power plants involves the splitting of the uranium-235 atom as shown in the following reaction.
In the example, the uranium-235 atom undergoes a transmutation into two distinct atoms, krypton and barium. It also releases 3 more free neutrons as well as energy. The energy released is used to heat water until it becomes steam. The steam is then used to rotate a coil of wire in a magnetic field, generating electrical energy. The 3 free neutrons are able to bombard 3 more uranium-235 atoms, causing additional fission reactions, which release even more neutrons. In power plants, the reaction is controlled. However, the number of free neutrons and subsequent fission reactions have the potential to grow exponentially in what is known as a chain reaction.
The main difference between radioactive decay and fission is that fission requires activation and produces free neutrons to continue the reaction. Radioactive decay occurs spontaneously and produces no free neutrons. Both reactions release energy.

How many neutrons are created in the following nuclear reaction?


The mass numbers and atomic numbers must remain constant. The arrow separating the reactants and products can be treated as an equal sign.
   Mass numbers: 235 + 1 = 90 + 143 + ?
Atomic numbers: 92 + 0 = 38 + 54 + ?
   The mass numbers on the product side of the reaction are missing 3 atomic mass units. Each neutron has a mass number of 1 atomic mass unit, so this fission reaction must produce 3 free neutrons

The fusion of two smaller atoms to become a larger atom requires a tremendous amount of activation energy to overcome the electrostatic repulsion of the protons. Unlike larger atoms, such as uranium-235 or uranium-238, which have a number of protons close together making it relatively easy to induce them to break apart, bringing small atoms together to make larger ones is quite difficult. An example of a fusion reaction is the fusion of two isotopes of hydrogen atoms into a helium atom:
   The isotopes of hydrogen in the above equation are known as deuterium and consist of 1 proton and 1 neutron. A fusion reaction will release more energy, per the mass of the reactants, than a fission reaction. However, inducing fusion is quite difficult because of the tremendous amount of energy needed to overcome the electrostatic repulsion of the two smaller reactant nuclei.
    The forces needed to drive these reactions occur naturally in stars, such as the Sun. The Sun is composed of an immense amount of gas (mostly hydrogen), and this huge amount of mass creates an enormous gravitational effect. As a result, these gases are under extreme temperature and pressure. In fact, they constitute a fourth state of matter known as plasma. These conditions provide the energy to initiate fusion reactions. Once running, fusion reactions produce significant amounts of excess energy.

Identifying Nuclear Reactions
Identify the nuclear process that is taking place in the following reaction.
   In fission reactions, the largest nucleus is on the reactant side (left side) of the reaction and it splits into smaller nuclei. In fusion reactions, the largest nucleus is on the product side (right side) of the reaction. The largest nucleus is 1-23, and it is on the product side. The reaction shown above is a fusion reaction. Note that this nucleus also appears to be an alpha particle. However, this is not an alpha decay. Alpha decay involves a larger nucleus ejecting an alpha particle. This reaction involves two small nuclei fusing to create the larger helium atom.


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