Chemistry 1050- Chapter 7: The Quantum-Mechanical Model of the Atom

Quantum-Mechanical Model of the Atom

A model that explains how electrons exist in atoms and how those electrons determine the chemical and physical properties of elements

Wave-Particle Duality

The idea that light and electrons have both wave-like and particle-like properties.

• Some behaviors are best explained as waves, while others are best explained as particles.

Electromagnetic Radiation

A wave made of oscillating electric and magnetic fields that are perpendicular to each other and move through space.

• In a vacuum, it travels at 3.00 × 10⁸ m/s.

Wavelength

The distance between adjacent crests(or troughs); in m, um, or nm

Frequency(v)

Number of wave cycles passing per second (s-1 or Hz)

Amplitude

The vertical height of the wave; related to intensity of light (bright = high, dim = low/small)

Electromagnetic Spectrum

The full range of electromagnetic radiation, including visible light, X-rays, microwaves, and more.

• It represents the classical wave model used to explain many observations in natural world

c = 3.0 × 10^8 m/s

The speed all waves in spectrum travel through vacuum

Monochromatic Light

Light of a single wavelength

Polychromatic Light

Light of many wavelengths( white light)

Diffraction and interference

Behaviours that occur when waves interact

Diffraction

Waves bending around obstacles (or slit) of comparable size

Interference

Interference is waves overlapping to strengthen or cancel each other depending on how they align.

Constructive Interference

Amplitudes add and the light becomes brighter

Destructive Interference

Waves/ Amplitude canceling each other (light becomes dim or dark)

Young’s Double Split Experiment

Scientists expected light to create two bright spots if it behaved like particles. Instead, it produced an interference pattern—multiple light and dark bands—showing that light behaves as interacting waves.

Blackbody Radiation

What kind of light/colour an object gives off depends only on its temperature. It doesn’t always appear black—its color changes with temperature because it emits different wavelengths of light. If the emitted light is outside the visible range, the object appears black to our eyes.

Classical Electromagnetic Theory

Predicted that radiation intensity would keep increasing without limit at very high frequencies (short wavelengths).

Max Planck

Explained blackbody radiation by proposing that energy is released in tiny, discrete packets called quantum (plural = quanta). This introduced the idea of quantized energy

The energy of each quantum is given by E = hν, where h (Planck’s constant) = 6.626 × 10⁻³⁴ J·s.

Quantized Energy

Energy occurs in fixed quantities, rather than being continuous

Photoelectric Effect

When shinning light of enough frequency on metal objects, it can eject electrons out of the metal. These freed electrons create an electric current.

Photon Theory

Einstein built on Planck’s idea. Proposed light is made of tiny energy packets called photons. Each photon has an energy that depends on its frequency, not the brightness (amplitude) of the light. (E=hv)

New Era of Physics

Beam of light is not a wave propagating through space but a shower of particles (E =hv)

Threshold Frequency Condition

Minium frequency of light to eject electrons from metal

Atomic Spectroscopy

The study of the light an element gives off when it is vaporized and excited by electricity.

Emission (line) Spectrum

When excited light from an element passes through a prism, it produces several sharp, coloured lines separated by dark spaces. Each element has its own unique pattern of lines.

Johannes Rydberg

A physicist who created the Rydberg equation, which predicts the wavelengths and positions of spectral lines in an element’s emission spectrum.

Rutherford’s Nuclear Model of the Atom

Atoms have a positive nucleus with negative electrons attracted to it. An electron’s motion provides enough kinetic energy to keep it from falling into the nucleus and negative potential energy from the nucleus keeps it from flying away.

Bohr Model of the Atom (Niels Bohr)

Developed a model of an atom to explain the atomic line spectra (based on planetary orbit idea). Built on Rutherford’s idea of electrons orbiting the nucleus like planets. Incorporated Planck’s and Einstein’s ideas of quantized energy, meaning electrons can only occupy specific energy levels.

Quantum Numbers and Electron Orbit

n = Positive integer associated with radius of electron orbit (Directly related to electron’s energy level in hydrogen atom). With lower the n value, the smaller the orbit’s radius representing lower energy orbit.

En = -2.18×10^-18 J (1/n²)

Ground State

Lowest(first) energy orbit. n=1, closest to the nucleus

Excited States

Electron in any orbit above ground state (n= 2, 3, 4,…)

Absorption

When an H atom absorbs a photon whose energy is equal to the difference between the lower and higher energy levels, it jumps to the higher (outer) energy level

Emission

When a H atom is in a higher energy level, and returns to a lower energy level (closer orbit) by emitting a photon whose energy is equal to the difference between the two levels.

De Broglie Wavelength

Proposed that all matter has a wavelength, and for electrons, this wave-like behavior helps explain why they occupy only specific energy levels in atoms.

Heisenberg’s Uncertainty Principle

It’s impossible to observe both the wave and particle nature of an electron simultaneously as you disturb one of them.These properties are complementary, meaning the more accurately you know one, the less accurately you can know the other.

Determinate Outcome

In classical physics (Newton’s laws), the present fully determines the future — outcomes are predictable.

Indeterminate Outcome

• In quantum mechanics, you cannot predict an exact future path for an electron. Instead, you can only determine the probability of where an electron is likely to be. These probabilities are shown as probability distribution maps.

Atomic Orbitals

Regions where electrons are most likely to be found.

Standing Waves

Waves that don’t travel; they stay in place and oscillate. If electrons behave like standing waves, they can have only certain fixed frequencies and energies.

Wave Function(Ψ)

A mathematical equation (often using sine or cosine) that describes a standing wave. In quantum mechanics, it describes the behaviour of an electron.

Orbital

A wave function in three-dimensional space for an electron. It shows the probable location of an electron. Essentially, it defines the spatial probability distribution where an electron is most likely to be found.

Schrödinger Equation

A mathematical equation that produces wave functions describing electrons in atoms. These wave functions can be used to create probability distribution maps, showing where an electron is likely to be for a given energy. Fully consistent with the Heisenberg Uncertainty Principle, since it predicts probabilities rather than exact positions.

Quantum Numbers

Used to describe orbitals that correspond to wave function solutions

Three Interrelated Quantum Numbers

1. n

2. l

3. ml

n

Principal quantum number. It is an integer determining overall size of orbital and indicates energy level of electron

l

Angular Momentum quantum number( azimuthal quantum number). Integer corresponds to orbital shape ( l = 0, 1, 2, 3, …, n-1)

ml

Magnetic quantum number. Integer corresponding to orientation of orbital (ml = -l + l)

2l + 1

Number of orbital in a sublevel

n²

Number of orbitals in principle level

S orbitals

l = 0. Lowest energy orbital, spherically symmetrical

Nodes

Radial (or spherical node), zero probability of finding an e-

n-1

Total nodes for any particular orbital

n-l-1

Total radial nodes

P orbitals

l =1. n = 2 or greater. Contains two lobes of electron density on either side of the nucleus with nodes located at the nucleus (Dumbbell shape)

Angular node

Planes, or surfaces where zero probability of finding e-. For an orbital, there are L angular nodes

D orbitals

l = 2. If n = 3 or greater, then principal level contains five d orbitals. 4/5 have clover shapes.

F orbitals

l = 3. If n = 4 or greater, then principal level contains seven f orbitals.

Quantum Theory

Describes the behaviour of e- in atoms. Helps to understand chemical behaviour.

Electron Configuration

Shows particular orbitals occupied for that atom

Electron Spin

Basic property of all e- and only two possibilités: +1/2 and -1/2

Pauli Exclusion Principle

No two electrons in an atom can have the same four quantum numbers

Degenerate Orbitals

Orbitals of the same energy level and depends only on the value of n (works for Hydrogen)

Multi-Electron Atoms

Energies of sub levels are split and depends on the value of l

Coulomb’s Law

The force between two charged particles depends on the size of their charges and the distance between them; like charges repel, and opposite charges attract.

Shielding

Electrons closer to te nucleus block some of the nucleus’s positive charge from reaching outer electrons. So, outer electrons don’t feel the full attraction of the nucleus.

Penetration

How close an electron in an orbital can get to the nucleus; orbitals that penetrate more feel a stronger attraction to the nucleus.

Aufbau Principle

Electrons fill the lowest available energy orbital first.

Pauli Exclusion Principle

Each orbital can hold a maximum of 2 electrons and they must have opposite spins

Hund’s Rule

Electrons will fill each orbital singly, with parallel spins, before they pair up

Ions

Atoms that have lost or gained electrons.

Electron configurations deduced from neutral atom and charge on ion:

i) anions – add number of electrons equal to magnitude of charge

ii) cations – subtract number of electrons equal to magnitude of charge

Paramagnetic

Have unpaired electrons which generate their own magnetic field and are attracted to an external magnetic field (Stern-Gerlach Experiment)

Diamagnetic

Paired electrons do not generate a magnetic field as they cancel each other’s spin. They are slightly repelled by a magnetic field but it’s weak.