Nuclear Reactions for the DAT
/Learn key DAT concepts about nuclear reactions, plus practice questions and answers
Everything you need to know about nuclear reactions for the dat
Table of Contents
Part 1: Introduction to nuclear reactions
Part 2: Binding energy
a) Nuclear structure
b) Components of the nucleus
Part 3: Decay processes and particles
a) Radioactive Decay
b) Alpha decay
c) Beta decay
d) Gamma decay
e) Balancing equations
Part 4: High-yield terms
Part 5: Questions and answers
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Part 1: Introduction to nuclear reactions
Nuclear reactions play a pivotal role in understanding the behavior of atomic nuclei. Unlike chemical reactions that involve changes in electron configurations, nuclear reactions involve alterations in the nucleus itself. These reactions typically manifest through processes such as nuclear fission (nucleus splitting apart) and fusion (nuclei joining together). As you study this guide, pay close attention to the high-yield bold terms.
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Part 2: Binding energy
An atom represents the tiniest entity of matter, constituting a chemical element. Initially perceived as the ultimate indivisible units of matter, it was later revealed that atoms could be deconstructed into fundamental charged particles—protons, neutrons, and electrons, with positive, neutral, and negative charges, respectively. The charge magnitude of a lone proton or electron is 1.6 x 10-19 C. Given that the charges of a single proton and electron are equivalent, when present in equal numbers, they yield a net charge of zero.
a) Nuclear structure
Atoms are composed of a central assembly of protons and neutrons, enveloped by electrons. This central assembly, known as the nucleus, was initially overlooked in early atomic models like J.J. Thompson’s "plum pudding" model. This model proposed an even distribution of protons, neutrons, and electrons throughout the atom, creating a uniform mixture where these particles appeared at the same density.
The Rutherford gold foil experiment played a pivotal role in reshaping the understanding of atomic structure. It demonstrated that a concentrated, positively charged mass—namely the nucleus—is situated at the atom's center. In this experiment, a thin sheet of gold foil was bombarded with positively charged alpha particles. If the plum pudding model were accurate, the alpha particles would have traversed the foil without deviation. Contrary to expectations, a fraction of the alpha particles underwent significant deflection, indicating the presence of a positively charged nucleus.
FIGURE 1: THE PLUM PUDDING MODEL’S PREDICTION AS COMPARED TO THE RESULTS OF THE GOLD FOIL EXPERIMENT
The Bohr Model emerged as a conceptual response following the revelations of the gold foil experiment. Prior to this experiment, J.J. Thompson had identified the presence of negatively charged electrons. Although these electrons seemed to occupy the outer regions of the atom, their precise location relative to the nucleus remained uncertain. The Bohr Model was subsequently introduced, suggesting that electrons revolve around the nucleus in orbits. This model drew an analogy between the atomic structure and the planetary system, portraying the nucleus as the sun, electrons as planets, and electrostatic attraction as the counterpart to gravitational attraction.
FIGURE 2: IN THE BOHR MODEL, ELECTRONS ORBIT THE NUCLEUS
Just as in planetary orbits, the energy of an electron plays a crucial role in determining its behavior. In planetary motion, a "lower energy" orbit corresponds to a smaller radius, experiencing a stronger gravitational pull, while a "higher energy" orbit involves a larger radius and a weaker gravitational pull. Stability is associated with lower energy orbits, whereas higher energy orbits are less stable. The Bohr model extends these principles to describe the dynamics of electrons.
A distinctive feature of the Bohr model, in contrast to planetary orbits, is the concept of quantized energy levels. These energy levels are not continuous but can only take on specific, discrete values. The orbiting electrons in a hydrogen atom must adhere to these quantized energy levels:
Note that -13.6 eV (electron volts) represents the energy of an electron in the ground state of a hydrogen atom. The specific energy value is dependent on the square of the atomic number and the Rydberg constant.
This energy, essentially, signifies the strength of the bond between the electron and nucleus. A more negative energy value corresponds to a more stable state. It's important to observe that higher values of n, the principal quantum number, result in less negative energy and therefore a less stable state. When the energy (E) reaches zero, the electron dissociates. For elements other than hydrogen, a more general equation replaces the numerator with the Rydberg constant (R) and the square of the atom's atomic number (Z2).
It is crucial to uphold the principle of energy conservation. Therefore, for an electron to transition between energy levels, it must either absorb or emit energy. According to the Bohr model, the emitted energy takes the form of electromagnetic radiation, most commonly visible light. Similarly, absorbed energy typically involves electromagnetic radiation. The type of light absorbed or emitted is linked to the change in energy level, as the energy content of light is associated with its frequency. Higher frequency light is closer to the blue end of the visible spectrum and possesses more energy than lower frequency light. Lower frequency light is in the red end of the spectrum. The energy of various frequencies of light is expressed by the formula:
Thus, when an electron absorbs blue light, it will jump up more energy levels than an electron that absorbs red light. The relationship between the wavelength of absorbed or emitted light and the change in energy level is given directly by the Rydberg formula:
FIGURE 3: VALENCE SHELL THEORY
The Bohr model, once prevalent among chemists, has been superseded by the valence shell theory for most applications. Nevertheless, it remains a sufficiently accurate approximation for many systems, especially the hydrogen atom, in understanding the intricate quantum mechanics at play.
b) Components of the nucleus
The nucleus of an atom, housing protons and neutrons, plays a critical role in defining the atom's key characteristics. The atomic number indicates the number of protons in the nucleus and uniquely identifies the element. Atoms with the same atomic number are of the same element. The total atomic mass encompasses both protons and neutrons, both of which have a mass of approximately 1 atomic mass unit (amu).
In contrast to the fixed number of protons, the count of neutrons within an element can vary. The variation in the number of neutrons leads to isotopes. Isotopes are often denoted by adding a dash and a number to the elemental symbol, representing the atomic mass of that isotope (e.g., O-16 with 8 protons and 8 neutrons). Elements with multiple stable isotopes may use the atomic weight, an average of the atomic masses of each stable isotope, which can be expressed as a decimal.
FIGURE 4: ATOMS AND THEIR PRESENTED INFORMATION
Nucleons, a collective term for protons and neutrons, are bound together with great strength by the powerful force within the nucleus known as the strong nuclear force. The energy needed to disassemble them completely is referred to as the binding energy of an atom, a value of considerable magnitude. Einstein's famous equation E=mc2 is applicable in this context, highlighting the conversion of a small mass (m) into an enormous amount of binding energy (E) due to the squared speed of light (c).
Surprisingly, the measured experimental mass of an atom often differs from the predicted mass obtained by summing the individual masses of nucleons. This variance accounts for the mass defect, where the experimental mass is consistently less than the predicted mass. The discrepancy arises because some mass is transformed into the immense energy that bonds the nucleons together within the nucleus.
The mass defect and, consequently, the binding energy, vary among different elements. Iron, with an atomic number of 56, exhibits the highest binding energy per nucleon.
In addition to the dominant strong nuclear force responsible for holding nucleons together within the nucleus, there is also a weaker force, aptly named the weak nuclear force. As its name implies, this force is considerably weaker than the strong nuclear force and has a more limited impact on the stability of subatomic particles.
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Part 3: Decay processes and particles
a) Radioactive decay
Isotopes of an element exhibit differences in stability, generally dictated by the number of neutrons. As a broad principle, isotopes with a neutron count approximately matching the atomic number tend to be more stable compared to their lighter counterparts.
Unstable isotopes possess the ability to undergo spontaneous decay processes, during which subatomic particles are emitted, resulting in the release of energy. There are three main types of radioactive decay: alpha, beta, and gamma radiation.
b) Alpha decay
The initial form of decay is alpha decay, wherein the unstable atom releases an alpha particle at a low velocity. An alpha particle comprises two protons and two neutrons, essentially resembling the nucleus of a helium atom. The reaction equation is as follows:
$${}^A_ZX\rightarrow Y + {}^4_2\alpha $$ $$ \mbox X\mbox{ = atomic number of original element,}$$ $$ Z \mbox{ = initial atomic number,}$$ $$Y \mbox{ = resulting element,}$$ $$\alpha \mbox{ = alpha particle, equivalent to a helium nucleus}$$
Alpha decay is the lowest energy radioactive decay. The emitted particle moves relatively slowly and can be stopped by something as thin as a piece of paper.
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