Quantum Theory of Atomic Structure CH3 by Owen Borville October 8, 2025
Energy is the capacity to do work or transfer heat. All forms of energy are either kinetic or potential.
Kinetic energy (Ek or KE) is the energy of motion.
KE or Ek = (1/2)mv² (where m is the mass of the object, v is the velocity)
One form of kinetic energy is thermal energy, which is the energy associated with the random motion of atoms and molecules.
Potential energy is the energy possessed by an object according to its position. There are two forms of potential energy in chemistry:
Chemical energy is the energy stored within the structural units of chemical substances. Electrostatic energy is the potential energy that results from the interaction of charged particles.
E(el) is proportional to (Q1Q2)/(d), where Q1 and Q2 represent two charges separated by a distance, d.
Kinetic and potential energy are interconvertible so that one can be converted to the other. Although energy can assume many forms, the total energy of the universe is constant. Energy can neither be created or destroyed. When energy of one form disappears, the same amount of energy reappears in another form or forms. This is known as the law of conservation of energy.
Units of Energy: the SI unit of energy in the joule (J), named after the English scientist James Joule. The joule is the amount of energy possessed by a 2 kg mass moving at a speed of 1 m/s.
Ek = 1/2mv² = 1/2 (2 kg)(1 m/s)² = 1 kg*m²/s² = 1 J
The joule can also be defined as the amount of energy exerted when a force of 1 newton (N) is applied over a distance of 1 m (1 J = 1 N * m)
Because the magnitude of a joule is so small, we often express large amounts of energy using the unit kilojoule (kJ). (1 kJ = 1000 J)
Visible light is only a small component of the continuum of radiant energy known as the electromagnetic spectrum.
Energy is the capacity to do work or transfer heat. All forms of energy are either kinetic or potential.
Kinetic energy (Ek or KE) is the energy of motion.
KE or Ek = (1/2)mv² (where m is the mass of the object, v is the velocity)
One form of kinetic energy is thermal energy, which is the energy associated with the random motion of atoms and molecules.
Potential energy is the energy possessed by an object according to its position. There are two forms of potential energy in chemistry:
Chemical energy is the energy stored within the structural units of chemical substances. Electrostatic energy is the potential energy that results from the interaction of charged particles.
E(el) is proportional to (Q1Q2)/(d), where Q1 and Q2 represent two charges separated by a distance, d.
Kinetic and potential energy are interconvertible so that one can be converted to the other. Although energy can assume many forms, the total energy of the universe is constant. Energy can neither be created or destroyed. When energy of one form disappears, the same amount of energy reappears in another form or forms. This is known as the law of conservation of energy.
Units of Energy: the SI unit of energy in the joule (J), named after the English scientist James Joule. The joule is the amount of energy possessed by a 2 kg mass moving at a speed of 1 m/s.
Ek = 1/2mv² = 1/2 (2 kg)(1 m/s)² = 1 kg*m²/s² = 1 J
The joule can also be defined as the amount of energy exerted when a force of 1 newton (N) is applied over a distance of 1 m (1 J = 1 N * m)
Because the magnitude of a joule is so small, we often express large amounts of energy using the unit kilojoule (kJ). (1 kJ = 1000 J)
Visible light is only a small component of the continuum of radiant energy known as the electromagnetic spectrum.
(NASA)
The speed of light (c) through a vacuum is a constant: c = 2.9979 x 10^8 meters/second, rounded to 3.00 x 10^8 m/s (300 million meters per second).
Speed of light, frequency, and wavelength are related: c = λν where λ, wavelength, is expressed in meters, and v, frequency, is expressed in reciprocal seconds (s-1)(or hertz, Hz)
Properties of Waves: All forms of electromagnetic radiation travel in waves. Waves are characterized by:
Wavelength (λ, lambda) the distance between identical points on successive waves.
Frequency (v, nu) the number of waves that pass through a particular point in 1 second.
Amplitude is the vertical distance from the midline of the wave to the top of the peak or the bottom of the trough.
An electromagnetic wave has both an electric field component and a magnetic component. The electric and magnetic components have the same frequency and wavelength.
The Double-Slit Experiment: When light passes through two closely spaced slits, an interference pattern is produced. Constructive interference is a result of adding waves that are in phase. Destructive interference is a result of adding waves that are out of phase. This type of interference is typical of waves and demonstrates the wave nature of light.
The speed of light (c) through a vacuum is a constant: c = 2.9979 x 10^8 meters/second, rounded to 3.00 x 10^8 m/s (300 million meters per second).
Speed of light, frequency, and wavelength are related: c = λν where λ, wavelength, is expressed in meters, and v, frequency, is expressed in reciprocal seconds (s-1)(or hertz, Hz)
Properties of Waves: All forms of electromagnetic radiation travel in waves. Waves are characterized by:
Wavelength (λ, lambda) the distance between identical points on successive waves.
Frequency (v, nu) the number of waves that pass through a particular point in 1 second.
Amplitude is the vertical distance from the midline of the wave to the top of the peak or the bottom of the trough.
An electromagnetic wave has both an electric field component and a magnetic component. The electric and magnetic components have the same frequency and wavelength.
The Double-Slit Experiment: When light passes through two closely spaced slits, an interference pattern is produced. Constructive interference is a result of adding waves that are in phase. Destructive interference is a result of adding waves that are out of phase. This type of interference is typical of waves and demonstrates the wave nature of light.
Double-Slit Experiment
Quantum Theory: Early attempts by 19th century physicists and scientists to figure out the structure of an atom only had limited success. These scientists were using the laws of classical physics, which are laws that describe the behavior of large, macroscopic objects. Later, scientists realized that the behavior of subatomic particles does not follow the same physical laws as larger objects.
Quantization of Energy: When a solid is heated, it emits electromagnetic radiation, known as blackbody radiation, over a wide range of wavelengths. The amount of energy given off at a certain temperature depends on the wavelength. Classical physics assumed that radiant energy was continuous, so that it could be emitted or absorbed in any amount.
Max Plank suggested that radiant energy is only emitted or absorbed in discrete quantities or bundles. A quantum of energy is the smallest quantity of energy that can be emitted or absorbed.
The energy E of a single quantum of energy is E = hv, where h is called Planck's constant, (6.63 x 10^-34 J * s).
Examples of quantized energy are the distinct atomic energy levels of electrons in an atom that can only exist as specific or certain energy values, like steps on a staircase. Other examples are photons, discrete packets of light energy with the energy depending on the frequency.
Photons and the Photoelectric Effect: Scientist Albert Einstein used Plank's theory to explain the photoelectric effect. Electrons are ejected from the surface of a metal exposed to light of a certain minimum frequency, called the threshold frequency. The number of electrons ejected is proportional to the intensity (or brightness) of the light. Below the threshold frequency no electrons are ejected, no matter how intense the light.
Einstein proposed that the beam of light is really a stream of particles. These particles of light are now called photons. Each photon must possess the energy given by the equation:
E (photon) = h v
Shining light onto a metal surface is like shooting a beam of particles or photons at the metal atoms. If the velocity of the photons equals the energy that binds the electrons in the metal, then the light will have enough energy to knock the electrons loose. High frequency is proportional to high energy. Therefore, light of higher frequency will knock the electrons loose and the electrons will also acquire some kinetic energy. This concept is shown by the equation:
hv = KE + W (where KE is the kinetic energy of the ejected electron and W is the binding energy of the electron).
Bohr's Theory of the Hydrogen Atom Sunlight is composed of various color components that can be recombined to produce white light. The emission spectrum of a substance can be seen buy energizing a sample of material with some form of energy. The red hot or white hod glow of an iron bar removed from a fire is the visible portion of its emission spectrum. The emission spectrum of both sunlight and a heated solid are continuous and all wavelengths of visible light are present.
Line spectra are the emission of light only at specific wavelengths. Every element has its own unique emission spectrum. The Rydberg equation can be used to calculate the wavelengths of the four visible lines in the emission spectrum of hydrogen.
1/λ = R∞ [(1/n1^2)-(1/n2^2)] where R∞ is the Rydberg constant (1.09737317 x 10^7 m-1), λ is the wavelength of a line in the spectrum, and n1 and n2 are positive integers, where n2 > n1.
Regarding the line spectrum of hydrogen, Neils Bohr attributed the emission of radiation by an energized hydrogen atom to the electron dropping from a higher-energy orbit to a lower one. As the electron dropped, it gave up a quantum of energy in the form of light. Bohr showed that energies of the electron in a hydrogen atom are given by the equation:
E(n) = -2.18 x 10^-18 J(1/n^2), where E(n) is the energy and n is a positive integer.
As an electron gets closer to the nucleus, n decreases. E(n) becomes larger in absolute value but more negative, as n gets smaller. E(n) is most negative when n = 1.
Called the ground state, this is the lowest energy state of the atom. For hydrogen, this is the most stable state. The stability of the electron decreases as n increases. Each energy state in which n > 1 is called an excited state.
Bohr's theory explains the line spectrum of the hydrogen atom. Radiant energy absorbed by the atom causes the electron to move from the ground state (n=1) to an excited state (n>1).
Conversely radiant energy is emitted when the electron moves from a higher-energy state to a lower energy excited state or the ground state. The quantized movement of the electron from one energy state to another is represented by a ball moving down steps.
n(i) is the initial state and n(f) is the final state
A photon is emitted when n(i) > n(f), ΔE is negative and energy is lost to the surroundings.
A photon is absorbed when n(f) >n(i), ΔE is positive.
The energy difference between the initial and final states is :
ΔE = hv = -2.18 x 10^-18 J (1/n(f)^2-1/n(i)^2)
To calculate wavelength, substitute c/λ for v and rearrange:
1/λ = (2.18 x 10^-18 J/hc) (1/n(f)^2-1/n(i)^2)
Since wavelength cannot be negative, the absolute value of the right side of the equation is taken and the negative sign is dropped.
Scientist Louis de Broglie reasoned that if light can behave like a stream of particles or photons, then electrons could exhibit wavelike properties.
According to de Broglie, electrons behave like standing waves. Only certain wavelengths are allowed. At a node the amplitude of the wave is zero.
The de Broglie Wave Hypothesis: De Broglie reasoned that the particle and wave properties are related by the following expression: λ = h/mv where λ is the wavelength associated with the particle, m is the mass (in kg) and v is the velocity in m/s. The wavelength calculated from this equation is known as the de Broglie wavelength.
Diffraction of Electrons: Experiments have shown that electrons do indeed possess wavelike properties. These experiments involved viewing the x-ray diffraction pattern of aluminum foil and the electron diffraction pattern of aluminum foil.
The Heisenberg uncertainty principle (by the German scientist Heisenberg) states that it is impossible to know simultaneously both the momentum p and the position x of a particle with certainty.
Δx * Δp >=h/4π, where Δx is the uncertainty in position in meters and Δp is the uncertainty in momentum.
Δx * mΔv >= h/4π, where Δv is the uncertainty in velocity in m/s and m is the mass in kg.
The Schrödinger Equation and the Quantum Mechanical Description of the Hydrogen Atom. Scientist Erwin Schrödinger derived a complex mathematical formula to incorporate the wave and particle characteristics of electrons. Wave behavior is described with the wave function ψ.
The probability of finding an electron in a certain area of space is proportional to ψ2 and is called electron density. Quantum mechanics defines the region where the electron is most likely to be at a given time.
The Schrödinger equation specifies possible energy states an electron can occupy in a hydrogen atom. The energy states and wave functions are characterized by a set of quantum numbers. Instead of referring to orbits as in the Bohr model, quantum numbers and wave functions describe atomic orbitals.
Quantum numbers are required to describe the distribution of electron density in an atom. There are three quantum numbers necessary to describe an atomic orbital.
The principal quantum number (n) designates size.
The angular momentum quantum number (l) describes shape.
The magnetic quantum number m(l) describes orientation.
The principal quantum number (n) designates the size of the orbital. Larger values of n correspond to larger orbitals. The allowed values of n are integral numbers: 1, 2, 3...The value of n corresponds to the value of n in Bohr's model of the hydrogen atom. A collection of orbitals with the same value of n is frequently called a shell.
The angular moment quantum number (l) describes the shape of the orbital. The values of (l) are integers that depend on the value of the principal quantum number. The allowed values of (l) range from 0 to n-1. Therefore, if n=2, (l) can be 0 or 1. A collection of orbitals with the same value of n and (l) is referred to as a subshell.
The magnetic quantum number m(l) describes the orientation of the orbital in space. The values of ml are integers that depend on the value of the angular moment quantum number: (-1,...0,...+1).
Quantum numbers designate shells, subshells, and orbitals.
The electron spin quantum number m(s) is used to specify an electron's spin. There are two possible directions of spin. Allowed values of m(s) are +1/2 and -1/2.
If a beam of atoms is split by a magnetic field., statistically, half of the electrons spin clockwise, the other half spin counterclockwise.
To summarize quantum numbers:
principal (n) = size
angular (l) = shape
magnetic m(l) = orientation
All three of these are required to describe an atomic orbital.
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principal (n=2)
angular momentum (l=1)
x = related to the magnetic quantum number m(l)
m(s) electron spin is the direction of spin and is required to describe an electron in an atomic orbital
All s orbitals are spherical in shape but differ in size.
1s<2s<3s
Principal quantum number (n=2)
2s
angular momentum quantum number (l) = 0
m(l) = 0; only one orientation possible.
The p orbitals= three orientations= l=1 (as required for a p orbital) m(l) = -1, 0, +1
The d orbitals= five orientations= l=2 (as required for a d orbital) m(l) = -2, -1, 0, +1, +2
The energies of the orbitals in the hydrogen atom depend only on the principal quantum number.
The electron configuration describes how the electrons are distributed in the various atomic orbitals. In a ground state hydrogen atom, the electron is found in the 1s orbital.
If hydrogen's electron is found in a higher energy orbital, the atom is in an excited state. A possible exited state electron configuration of hydrogen is 2s1.
The helium emission spectrum is more complex than the hydrogen spectrum. There are more possible energy transitions in a helium atom because helium has two electrons.
In multielectron atoms, the energies of the atomic orbitals are split. The splitting of the energy levels refers to the splitting of a shell (n=3) into subshells of different energies (3s, 3p, 3d).
The Pauli Exclusion Principle states that no two electrons in an atom can have the same four quantum numbers.
The Aufbau Principle states that electrons are added to the lowest energy orbitals first before moving to higher energy orbitals.
Li has a total of three electrons. So the third electron must go in the next available orbital with the lowest possible energy. The 1s orbital can only accommodate two electrons, according to the Pauli exclusion principle.
The ground state electron configuration of Li is 1s²2s¹
Be (Beryllium) has a total of four electrons. The ground state electron configuration of Be is 1s²2s²
B (Boron) has a total of five electrons. The ground state electron configuration of B is 1s² 2s² 2p¹
Hund's Rule states that the most stable arrangement of electrons is the one in which the number of electrons with the same spin is maximized.
C (Carbon) has a total of six electrons. The ground state electron configuration is 1s²2s²2p² One electron goes into each of the first two 2p orbitals before pairing, according to Hund's rule. The 2p orbitals are of equal energy or degenerate.
N (nitrogen) has seven electrons. The ground state electron configuration is 1s²2s²2p³ One electron goes into each 2p orbital before pairing.
O (Oxygen) has eight electrons. The ground state electron configuration is 1s²2s²2p⁴ Once all the 2p orbitals are singly occupied, additional electrons will have to pair with those already in the orbitals.
F (Fluorine) has nine electrons. The ground state electron configuration is 1s²2s²2p⁵. When there are one or more unpaired electrons, as in the case of oxygen and fluorine, the atom is called paramagnetic.
Ne (Neon) has ten electrons. The ground state electron configuration is 1s²2s²2p⁶. When all of the electrons in an atom are paired, as in neon, it is called diamagnetic.
General Rules for Writing Electron Configurations:
(1) Electrons will reside in the available orbitals of the lowest possible energy. (2) Each orbital can accommodate a maximum of two electrons. (3) Electrons will not pair in degenerate orbitals if an empty orbital is available.
The electron configurations of all elements except hydrogen and helium can be represented using a noble gas core for simplicity and avoiding repetition.
The noble gas configuration of Potassium (Z=19) is= [Ar] 4s¹
Argon's electron configuration is 1s²2s²2p⁶3s²3p⁶ so this is added to the end of potassium's electron configuration. Written out in full, this is the electron configuration of Potassium. 1s²2s²2p⁶3s²3p⁶4s¹
At the center of the Periodic Table, from Sc to Zn on the top row and everything below is the transition metal elements, or transition metals.
Chromium and Copper have slightly different electron configurations (or exceptions to the Aufbau principle) because of slightly greater stability of d subshells that are half-filled or completely filled over the s subshell.
Chromium [Ar] 3d⁵ 4s¹
Copper [Ar] 3d¹⁰ 4s¹
Quantization of Energy: When a solid is heated, it emits electromagnetic radiation, known as blackbody radiation, over a wide range of wavelengths. The amount of energy given off at a certain temperature depends on the wavelength. Classical physics assumed that radiant energy was continuous, so that it could be emitted or absorbed in any amount.
Max Plank suggested that radiant energy is only emitted or absorbed in discrete quantities or bundles. A quantum of energy is the smallest quantity of energy that can be emitted or absorbed.
The energy E of a single quantum of energy is E = hv, where h is called Planck's constant, (6.63 x 10^-34 J * s).
Examples of quantized energy are the distinct atomic energy levels of electrons in an atom that can only exist as specific or certain energy values, like steps on a staircase. Other examples are photons, discrete packets of light energy with the energy depending on the frequency.
Photons and the Photoelectric Effect: Scientist Albert Einstein used Plank's theory to explain the photoelectric effect. Electrons are ejected from the surface of a metal exposed to light of a certain minimum frequency, called the threshold frequency. The number of electrons ejected is proportional to the intensity (or brightness) of the light. Below the threshold frequency no electrons are ejected, no matter how intense the light.
Einstein proposed that the beam of light is really a stream of particles. These particles of light are now called photons. Each photon must possess the energy given by the equation:
E (photon) = h v
Shining light onto a metal surface is like shooting a beam of particles or photons at the metal atoms. If the velocity of the photons equals the energy that binds the electrons in the metal, then the light will have enough energy to knock the electrons loose. High frequency is proportional to high energy. Therefore, light of higher frequency will knock the electrons loose and the electrons will also acquire some kinetic energy. This concept is shown by the equation:
hv = KE + W (where KE is the kinetic energy of the ejected electron and W is the binding energy of the electron).
Bohr's Theory of the Hydrogen Atom Sunlight is composed of various color components that can be recombined to produce white light. The emission spectrum of a substance can be seen buy energizing a sample of material with some form of energy. The red hot or white hod glow of an iron bar removed from a fire is the visible portion of its emission spectrum. The emission spectrum of both sunlight and a heated solid are continuous and all wavelengths of visible light are present.
Line spectra are the emission of light only at specific wavelengths. Every element has its own unique emission spectrum. The Rydberg equation can be used to calculate the wavelengths of the four visible lines in the emission spectrum of hydrogen.
1/λ = R∞ [(1/n1^2)-(1/n2^2)] where R∞ is the Rydberg constant (1.09737317 x 10^7 m-1), λ is the wavelength of a line in the spectrum, and n1 and n2 are positive integers, where n2 > n1.
Regarding the line spectrum of hydrogen, Neils Bohr attributed the emission of radiation by an energized hydrogen atom to the electron dropping from a higher-energy orbit to a lower one. As the electron dropped, it gave up a quantum of energy in the form of light. Bohr showed that energies of the electron in a hydrogen atom are given by the equation:
E(n) = -2.18 x 10^-18 J(1/n^2), where E(n) is the energy and n is a positive integer.
As an electron gets closer to the nucleus, n decreases. E(n) becomes larger in absolute value but more negative, as n gets smaller. E(n) is most negative when n = 1.
Called the ground state, this is the lowest energy state of the atom. For hydrogen, this is the most stable state. The stability of the electron decreases as n increases. Each energy state in which n > 1 is called an excited state.
Bohr's theory explains the line spectrum of the hydrogen atom. Radiant energy absorbed by the atom causes the electron to move from the ground state (n=1) to an excited state (n>1).
Conversely radiant energy is emitted when the electron moves from a higher-energy state to a lower energy excited state or the ground state. The quantized movement of the electron from one energy state to another is represented by a ball moving down steps.
n(i) is the initial state and n(f) is the final state
A photon is emitted when n(i) > n(f), ΔE is negative and energy is lost to the surroundings.
A photon is absorbed when n(f) >n(i), ΔE is positive.
The energy difference between the initial and final states is :
ΔE = hv = -2.18 x 10^-18 J (1/n(f)^2-1/n(i)^2)
To calculate wavelength, substitute c/λ for v and rearrange:
1/λ = (2.18 x 10^-18 J/hc) (1/n(f)^2-1/n(i)^2)
Since wavelength cannot be negative, the absolute value of the right side of the equation is taken and the negative sign is dropped.
Scientist Louis de Broglie reasoned that if light can behave like a stream of particles or photons, then electrons could exhibit wavelike properties.
According to de Broglie, electrons behave like standing waves. Only certain wavelengths are allowed. At a node the amplitude of the wave is zero.
The de Broglie Wave Hypothesis: De Broglie reasoned that the particle and wave properties are related by the following expression: λ = h/mv where λ is the wavelength associated with the particle, m is the mass (in kg) and v is the velocity in m/s. The wavelength calculated from this equation is known as the de Broglie wavelength.
Diffraction of Electrons: Experiments have shown that electrons do indeed possess wavelike properties. These experiments involved viewing the x-ray diffraction pattern of aluminum foil and the electron diffraction pattern of aluminum foil.
The Heisenberg uncertainty principle (by the German scientist Heisenberg) states that it is impossible to know simultaneously both the momentum p and the position x of a particle with certainty.
Δx * Δp >=h/4π, where Δx is the uncertainty in position in meters and Δp is the uncertainty in momentum.
Δx * mΔv >= h/4π, where Δv is the uncertainty in velocity in m/s and m is the mass in kg.
The Schrödinger Equation and the Quantum Mechanical Description of the Hydrogen Atom. Scientist Erwin Schrödinger derived a complex mathematical formula to incorporate the wave and particle characteristics of electrons. Wave behavior is described with the wave function ψ.
The probability of finding an electron in a certain area of space is proportional to ψ2 and is called electron density. Quantum mechanics defines the region where the electron is most likely to be at a given time.
The Schrödinger equation specifies possible energy states an electron can occupy in a hydrogen atom. The energy states and wave functions are characterized by a set of quantum numbers. Instead of referring to orbits as in the Bohr model, quantum numbers and wave functions describe atomic orbitals.
Quantum numbers are required to describe the distribution of electron density in an atom. There are three quantum numbers necessary to describe an atomic orbital.
The principal quantum number (n) designates size.
The angular momentum quantum number (l) describes shape.
The magnetic quantum number m(l) describes orientation.
The principal quantum number (n) designates the size of the orbital. Larger values of n correspond to larger orbitals. The allowed values of n are integral numbers: 1, 2, 3...The value of n corresponds to the value of n in Bohr's model of the hydrogen atom. A collection of orbitals with the same value of n is frequently called a shell.
The angular moment quantum number (l) describes the shape of the orbital. The values of (l) are integers that depend on the value of the principal quantum number. The allowed values of (l) range from 0 to n-1. Therefore, if n=2, (l) can be 0 or 1. A collection of orbitals with the same value of n and (l) is referred to as a subshell.
The magnetic quantum number m(l) describes the orientation of the orbital in space. The values of ml are integers that depend on the value of the angular moment quantum number: (-1,...0,...+1).
Quantum numbers designate shells, subshells, and orbitals.
The electron spin quantum number m(s) is used to specify an electron's spin. There are two possible directions of spin. Allowed values of m(s) are +1/2 and -1/2.
If a beam of atoms is split by a magnetic field., statistically, half of the electrons spin clockwise, the other half spin counterclockwise.
To summarize quantum numbers:
principal (n) = size
angular (l) = shape
magnetic m(l) = orientation
All three of these are required to describe an atomic orbital.
2px
principal (n=2)
angular momentum (l=1)
x = related to the magnetic quantum number m(l)
m(s) electron spin is the direction of spin and is required to describe an electron in an atomic orbital
All s orbitals are spherical in shape but differ in size.
1s<2s<3s
Principal quantum number (n=2)
2s
angular momentum quantum number (l) = 0
m(l) = 0; only one orientation possible.
The p orbitals= three orientations= l=1 (as required for a p orbital) m(l) = -1, 0, +1
The d orbitals= five orientations= l=2 (as required for a d orbital) m(l) = -2, -1, 0, +1, +2
The energies of the orbitals in the hydrogen atom depend only on the principal quantum number.
The electron configuration describes how the electrons are distributed in the various atomic orbitals. In a ground state hydrogen atom, the electron is found in the 1s orbital.
If hydrogen's electron is found in a higher energy orbital, the atom is in an excited state. A possible exited state electron configuration of hydrogen is 2s1.
The helium emission spectrum is more complex than the hydrogen spectrum. There are more possible energy transitions in a helium atom because helium has two electrons.
In multielectron atoms, the energies of the atomic orbitals are split. The splitting of the energy levels refers to the splitting of a shell (n=3) into subshells of different energies (3s, 3p, 3d).
The Pauli Exclusion Principle states that no two electrons in an atom can have the same four quantum numbers.
The Aufbau Principle states that electrons are added to the lowest energy orbitals first before moving to higher energy orbitals.
Li has a total of three electrons. So the third electron must go in the next available orbital with the lowest possible energy. The 1s orbital can only accommodate two electrons, according to the Pauli exclusion principle.
The ground state electron configuration of Li is 1s²2s¹
Be (Beryllium) has a total of four electrons. The ground state electron configuration of Be is 1s²2s²
B (Boron) has a total of five electrons. The ground state electron configuration of B is 1s² 2s² 2p¹
Hund's Rule states that the most stable arrangement of electrons is the one in which the number of electrons with the same spin is maximized.
C (Carbon) has a total of six electrons. The ground state electron configuration is 1s²2s²2p² One electron goes into each of the first two 2p orbitals before pairing, according to Hund's rule. The 2p orbitals are of equal energy or degenerate.
N (nitrogen) has seven electrons. The ground state electron configuration is 1s²2s²2p³ One electron goes into each 2p orbital before pairing.
O (Oxygen) has eight electrons. The ground state electron configuration is 1s²2s²2p⁴ Once all the 2p orbitals are singly occupied, additional electrons will have to pair with those already in the orbitals.
F (Fluorine) has nine electrons. The ground state electron configuration is 1s²2s²2p⁵. When there are one or more unpaired electrons, as in the case of oxygen and fluorine, the atom is called paramagnetic.
Ne (Neon) has ten electrons. The ground state electron configuration is 1s²2s²2p⁶. When all of the electrons in an atom are paired, as in neon, it is called diamagnetic.
General Rules for Writing Electron Configurations:
(1) Electrons will reside in the available orbitals of the lowest possible energy. (2) Each orbital can accommodate a maximum of two electrons. (3) Electrons will not pair in degenerate orbitals if an empty orbital is available.
The electron configurations of all elements except hydrogen and helium can be represented using a noble gas core for simplicity and avoiding repetition.
The noble gas configuration of Potassium (Z=19) is= [Ar] 4s¹
Argon's electron configuration is 1s²2s²2p⁶3s²3p⁶ so this is added to the end of potassium's electron configuration. Written out in full, this is the electron configuration of Potassium. 1s²2s²2p⁶3s²3p⁶4s¹
At the center of the Periodic Table, from Sc to Zn on the top row and everything below is the transition metal elements, or transition metals.
Chromium and Copper have slightly different electron configurations (or exceptions to the Aufbau principle) because of slightly greater stability of d subshells that are half-filled or completely filled over the s subshell.
Chromium [Ar] 3d⁵ 4s¹
Copper [Ar] 3d¹⁰ 4s¹
