Atomic and Nuclear Physics for the MCAT: Everything You Need to Know
/Learn key MCAT concepts about atomic and nuclear physics, plus practice questions and answers
(Note: This guide is part of our MCAT Physics series.)
Table of Contents
Part 1: Introduction to atomic and nuclear physics
Part 2: Atomic structure
a) Nuclear structure
b) Components of the nucleus
Part 3: Radioactive decay
a) Alpha decay
b) Beta decay
c) Gamma decay
d) Half-life and exponential decay
Part 4: High-yield terms and equations
Part 5: Passage-based questions and answers
Part 6: Standalone questions and answers
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Part 1: Introduction to atomic and nuclear physics
Atomic and nuclear physics is a wide-ranging topic that covers the structure and behavior of the individual atom. In this guide, we’ll focus on the most important experimental results and the equations that came to describe some of those results.
On the MCAT, atomic and nuclear physics is a medium-yield topic. Getting these concepts down will help you ace any related questions on the test and might even provide some intuition on chemistry and molecular biology topics, too.
Similar to our other guides, the most important terms below are in bold font. When you see one, try to define it in your own words and use it to create your own examples. This is a great way to check your understanding, and phrasing things in a way that makes the most sense to you will make studying much easier (and much more effective!) in the long run.
Let’s get started!
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Part 2: Atomic structure
a) Nuclear structure
Atoms consist of a central cluster of protons and neutrons surrounded by electrons. The central cluster of protons and neutrons is called the nucleus. Early models of the atom, such as J.J. Thompson’s “plum pudding” model, did not include the nucleus and instead proposed that protons, neutrons, and electrons were evenly distributed throughout the atom. Under the plum pudding model, these three types of particles would be homogeneously mixed about and appear to be present at the same density.
Rutherford gold foil experiment
The Rutherford gold foil experiment showed that a dense, positively charged clump of mass must be located at the center of an atom.
The experimental setup consisted of a very thin sheet of gold foil and a device that would shoot positively charged alpha particles at the foil. (More on alpha particles later, but suffice to say that they are positively charged particles.) If the plum pudding model were correct, the alpha particles would have passed through the foil with no deflection. However, to the researchers’ surprise, a small proportion of the alpha particles experienced a very strong deflection. This suggested the existence of a positively charged nucleus.
Figure: The plum pudding model’s prediction as compared to the results of the gold foil experiment
The Bohr Model
By the time the results of the gold foil experiment were known, J.J. Thompson had already discovered the existence of negatively charged electrons. These electrons appeared to exist on the periphery of the atom, but no one had definitively proven their location around the nucleus. This inference was eventually developed into the Bohr Model of the atom, which proposed that electrons orbited the nucleus. This model was analogous to the orbits of planets in our Solar System, where the nucleus was substituted for the sun, electrons for the planets, and electrostatic attraction for gravitational attraction.
Figure: In the Bohr model, electrons orbit the nucleus.
Just like planetary orbits, the energy of an electron affects its dynamics. In planetary orbit, a “lower energy” orbit refers to an orbit with a smaller radius that feels a stronger gravitational pull, while a “higher energy” orbit refers to an orbit with a larger radius that feels a weaker gravitational pull. A lower energy orbit is more stable, and a higher energy orbit is less stable. The same principles apply to electron orbit under the Bohr model.
A key difference from planetary orbits is that the Bohr model states that the possible energy levels are quantized, meaning they are not continuous and can only be certain numbers. The energy levels of the orbiting electrons in a hydrogen atom must follow:
$$ E = -\frac{13.6\space eV}{n^2}$$ $$\mbox{where } E\mbox{ = energy,} $$ $$n \mbox{ = energy level of the electron}$$
Note that -13.6 eV (electron volts) is the energy of an electron in the ground state of a hydrogen atom. (In general, this energy depends on the square of the atomic number and the Rydberg constant.)
Remember that energy must always be conserved. So, in order for the electron to change energy levels, it needs to either absorb energy or emit energy. The Bohr model specifies that emitted energy is in the form of electromagnetic radiation: most commonly, emitted as visible light. In general, the absorbed energy tends to be electromagnetic radiation, too.
The type of light absorbed or emitted by the electron is related to the change in energy level because the energy contained in light depends on its frequency. Higher frequency light (or colors that are closer to the color blue in the visible spectrum) has more energy than lower frequency light (like the color red in the visible spectrum). The energy of different frequencies of light is given by:
$$ E = h\nu = h\frac{c}{\lambda}$$ $$\mbox{where }E\mbox{ = energy,}$$ $$h\mbox{ = Planck's constant, equal to } 6.6\times 10^{-34}\space {}^{m^2\space kg/}{}_s$$ $$\nu \mbox{ = frequency of light,}$$ $$c \mbox{ = speed of light in a vacuum, equal to } 3\times10^8 \space {}^m/_s$$ $$\lambda \mbox{ = wavelength of the light}$$
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:
$$ \frac{1}{\lambda}=R_H(\frac{1}{n_f^2} -\frac{1}{n_i^2})$$ $$\mbox{where } \lambda \mbox{ = wavelength of the light,}$$ $$ R_H \mbox{ = the Rydberg constant, equal to }1.09\times 10^7 \space m^{-1}$$ $$n_f \mbox{ = final energy level,}$$ $$n_i \mbox{ = initial energy level}$$
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