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Introduction
1. CARS
2. Psych/soc
3. Bio/biochem
4. Chem/phys
4.1 4A: Translational motion, forces, work, energy, and equilibrium
4.2 4B: Fluids in circulation of blood, gas movement, and gas exchange
4.3 4C: Electrochemistry and electrical circuits and their elements
4.4 4D: How light and sound interact with matter
4.5 4E: Atoms, nuclear decay, electronic structure, and atomic chemical behavior
4.5.1 Atomic nucleus and electronic structure
4.5.2 Stoichiometry
4.5.3 The periodic table
4.6 5A: Unique nature of water and its solutions
4.7 5B: Nature of molecules and intermolecular interaction
4.8 5C: Separation and purification methods
4.9 5D: Structure, function, and reactivity of bio-relevant molecules
4.10 5E: Principles of chemical thermodynamics and kinetics, enzymes
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4.5.1 Atomic nucleus and electronic structure
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4. Chem/phys
4.5. 4E: Atoms, nuclear decay, electronic structure, and atomic chemical behavior
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Atomic nucleus and electronic structure

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Atomic number, atomic weight

The atomic number represents the number of protons in an atom’s nucleus and is fundamental in defining an element; if two atoms have the same atomic number, they are the same element.

In contrast, the atomic weight is the weighted average of the atomic masses (the sum of protons and neutrons) of all the isotopes of that element. In standard atomic notation, the atomic number appears as a subscript (at the bottom) while the atomic weight is shown as a superscript (at the top), emphasizing that the atomic number forms the foundation of an element’s identity.

Neutrons, protons, isotopes

Neutrons are neutral particles found in the nucleus of an atom, while protons are positively charged particles also located in the nucleus. Together, these particles are known as nucleons and contribute significantly to an atom’s mass.

Isotopes are different forms of an element that have the same number of protons (and therefore the same atomic number) but vary in their number of neutrons, resulting in different atomic masses. For instance, a proton has a mass of about 1 atomic mass unit (amu) and a +1 charge, a neutron also weighs approximately 1 amu but carries no charge, and electrons, which orbit the nucleus, have negligible mass and a -1 charge. This difference in neutron count means that while isotopes exhibit nearly identical chemical properties, their nuclear stability can vary; some are stable, while others may undergo radioactive decay.

Nuclear forces, binding energy

In the nucleus, two fundamental forces are at play: the strong force, which binds nucleons together and contributes to the binding energy, and the electromagnetic force, which causes repulsion between the positively charged protons. The nucleus remains intact because the strong force is significantly stronger than the electromagnetic repulsion.

Binding energy usually refers to nuclear binding energy, which is the energy that holds nucleons together within the nucleus. This energy arises from the strong force. The binding energy per nucleon is a measure of a nucleus’s stability; for example, Iron-56 has one of the highest values, making it very stable, whereas Deuterium (a two-nucleon isotope of hydrogen) has one of the lowest. Additionally, electron binding energy, more commonly known as ionization energy, is the energy required to remove an electron from an atom.

Radioactive decay

Radioactive decay is the process by which unstable nuclei release energy by emitting particles or radiation. There are three primary types:

  1. Alpha decay, where an alpha particle (a helium nucleus) is emitted at low speed
  2. Beta decay, which involves the ejection of a high-speed electron known as a beta particle
  3. Gamma decay, where a high-energy gamma ray (an electromagnetic wave) is released.

These decay processes adhere to conservation laws, ensuring that the total atomic weight and atomic number remain constant before and after the decay.

Half-life, exponential decay, semi-log plots, fission and fusion

Stability refers to the tendency of a substance to resist decay; a stable substance does not decay, whereas an unstable one undergoes decay, with a shorter half-life indicating greater instability. The standard half-life equation relates the remaining amount of material (Nₜ) to the initial quantity (N₀) and the elapsed time (t), and alternative forms of this equation are sometimes used for more convenient calculations. This decay typically follows an exponential pattern, meaning the amount of the substance decreases by a constant fraction over equal time intervals. To analyze exponential decay, a semi-log plot is used, which graphs the logarithm of the remaining quantity versus time; in such a plot, exponential decay appears as a straight line with a negative slope that intercepts the x-axis when the initial quantity equals one.

In nuclear reactions, fission is the process where a heavy nucleus splits into smaller nuclei upon being struck by a free neutron, releasing additional neutrons that can trigger a chain reaction, as seen in uranium. Conversely, fusion involves the combining of two nuclei, and this process powers the sun by fusing hydrogen atoms into helium.

Mass spectrometer

A mass spectrometer is an analytical instrument that measures the mass-to-charge ratio of ionized particles. First, the sample is ionized in the ion source, converting its molecules into charged particles. These ions are then accelerated by an electric field and enter a mass analyzer, where they are deflected by a magnetic field according to their mass-to-charge ratio. Lighter ions are deflected more than heavier ones, allowing them to be separated and detected by the detector. The resulting mass spectrum provides detailed information about the molecular structure, composition, and abundance of the sample, making mass spectrometry a crucial tool in fields such as chemistry, biochemistry, and environmental science.

Electronic structure

In the hydrogen atom, the electron’s arrangement is described by its orbital structure. While the Bohr model depicted the electron as orbiting the nucleus in fixed paths, quantum mechanics shows that the electron exists within a spherical probability cloud around the nucleus.

The principal quantum number (n) defines the shell in which the electron resides, with n starting at 1 and increasing for higher energy levels. Each shell contains n2 orbitals, and since each orbital can accommodate 2 electrons, the maximum number of electrons per shell is 2n2.

Ground state, excited states, absorption and emission line spectra

In an atom, electrons typically reside in the ground state, which is the lowest possible energy level. When electrons absorb energy, they become excited, moving to higher energy levels known as excited states. These states are energetically less favorable than the ground state, so electrons tend to return to the ground state by releasing the absorbed energy as light.

This process of energy absorption and emission produces characteristic absorption spectra and emission spectra. An absorption spectrum appears as a series of dark lines on a continuous rainbow background, indicating the wavelengths of light that have been absorbed by the atom. Conversely, an emission spectrum displays* bright, colored lines* on a dark background, corresponding to the wavelengths of light emitted as electrons fall back to lower energy levels. Notably, the pattern of lines in the absorption spectrum closely matches that of the emission spectrum, although the emitted wavelengths are often slightly longer.

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Quantum numbers and quantum states

Quantum numbers describe the allowed states for electrons in an atom. The angular momentum quantum number (l), which ranges from 0 to n−1, determines the shape of the orbital and is associated with subshell labels: s for l=0, p for l=1, d for l=2, and f for l=3. Each subshell contains a specific number of orbitals—one in the s-subshell, three in the p-subshell, five in the d-subshell, and seven in the f-subshell—and since each orbital holds up to two electrons, a subshell can accommodate up to 4l+2 electrons.

The magnetic quantum number (m), which takes on integer values from –l to +l, specifies the orientation of an orbital in space. Finally, the spin quantum number (s) indicates the intrinsic angular momentum of an electron, with possible values of +1/2 or –1/2. Together, these quantum numbers define the complete quantum state of an electron in an atom.

Paramagnetism and diamagnetism

Paramagnetism occurs in materials that have unpaired electrons, which give rise to a net magnetic moment. When exposed to an external magnetic field, these materials are attracted to it due to the alignment of their magnetic moments.

In contrast, diamagnetism is a property of materials where all electrons are paired, resulting in no permanent magnetic moment. When placed in a magnetic field, these materials produce an induced magnetic field that opposes the applied field, causing a weak repulsion.

Conventional notation for electronic structure

Conventional notation for electronic structure, often shown in an orbital diagram, uses a set of rules to describe how electrons are arranged in atoms.

  • The Aufbau principle dictates that electrons fill shells and subshells in order of increasing energy; for example, the 1s orbital is filled before 2s, and 2p follows next, with d subshells being filled after the corresponding s orbital.
  • Hund’s rule states that in any subshell containing multiple orbitals (such as p,d, or f), electrons are distributed one per orbital with the same spin until every orbital is half-filled, which minimizes electron-electron repulsion.
  • The Pauli exclusion principle requires that no two electrons in the same orbital can have identical spin; they must have opposite spins. Special cases occur in elements with d subshells, such as those with d⁴ and d⁹ configurations, where achieving a half-full or fully filled d subshell (for example, as in s1d5 or s1d10) is favored for increased stability.

Bohr atom and effective nuclear charge

The Bohr atom model depicts electrons as moving in fixed circular orbits around the nucleus, with the orbit size increasing as the principal quantum number (n) increases. This model provides a simple visualization of electron positions in atoms.

The effective nuclear charge is the net positive charge experienced by an electron. It is calculated by subtracting the shielding provided by shielding electrons (those in inner, lower-energy orbitals) from the total nuclear charge. A higher effective nuclear charge means that an electron is held more tightly by the nucleus, leading to increased ionization energy and overall atomic stability. As you move from left to right across a period in the periodic table, the effective nuclear charge for outer electrons typically increases.

Heisenberg uncertainty principle

The Heisenberg Uncertainty Principle establishes a fundamental limit to the simultaneous precision with which certain pairs of properties—such as position and momentum—can be known. In essence, the more accurately one of these properties is measured, the less precisely the other can be determined. This concept also applies to other pairs of canonically conjugate variables like energy and time. For example, when you try to measure a particle’s location with high accuracy, the uncertainty in its momentum increases, and vice versa. This intrinsic limit is quantitatively expressed by an inequality involving the standard deviations of these variables, with the lower bound set by Planck’s constant (6.62607015×10−34 joule second).

Photoelectric effect

The photoelectric effect occurs when light hits a metal surface, causing electrons—called photoelectrons—to be ejected. This phenomenon, also known as photoemission, happens when the energy of an incoming photon (E₍photon₎), determined by Planck’s equation E(​photon)​ = hν (where h is Planck’s constant and ν is the frequency), sufficient to overcome the metal’s work function (Φ). The work function is the energy required to free an electron from the metal.

Any excess energy becomes the kinetic energy (KE(​electron)​) of the ejected electron, expressed as KE(​electron)​ = hν−Φ. This equation shows that the kinetic energy increases linearly with the frequency of the light, provided the photon energy exceeds the work function. Additionally, the kinetic energy can be related to the electron’s velocity (v) using the formula KE(​electron)​=½m(​e)​v2, where m(​e)​ is the electron’s mass.

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