Quantum Theory and the Electronic Structure of Atoms

Max Planck

- Discovered atoms and molecules emit energy in quantities he called quanta (bundle of energy)

- Revived the "Wave Theory of Energy"

Wavelength (lambda)

The distance between identical points on successive waves

Amplitude

The vertical distance from the midline of a wave to the peak or trough

Frequency (nu)

- The number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s).

-The higher the frequency the higher the energy, the lower the frequency the lower the energy

Speed (u)

wavelength times frequency

Electromagnetic Radiation

the emission and transmission of energy in the form of electromagnetic waves

James Maxwell

proposed that visible light consists of electromagnetic waves

Speed of light (c) in vacuum

3.00e8 m/s

Speed of electromagnetic radiation

wavelength * frequency = speed of light

Regions of the Electromagnetic Spectrum (in order)

gamma ray, x-ray, UV, visible, infrared, microwave, radio frequency

Colors of the Electromagnetic Spectrum (in order)

blue, green, yellow, orange, red

(400 to 750 in wavelength) (7.5e14 to 4.0e14 in frequency)

Blackbody Radiation

When solids are heated, they emit electromagnetic radiation over a wide range of wavelengths

Planck's Quantum Theory

- Quantum - the smallest quantity of energy that can be emitted (or absorbed) in the form of electromagnetic radiation

- Energy can be gained or lost only in whole-number multiples

Planck's Constant (H)

6.626e-34 J/s

Photoelectric Effect

- Electrons are ejected from the surface of certain metals exposed to light of a certain minimum frequency, called the threshold frequency

- The number of electrons ejected was proportional to the brightness (intensity) but not to the energy of the electron.

- Einstein suggested that light was a stream of particles called photons.

- The Photon had to carry enough energy so that the electron could absorb the energy and become free from the surface of the metal.

Einstein's Theory of Light

EMR can be viewed as a stream of discrete particles called photons. This theory is in direct conflict with the wave theory.

Photon Energy

E = hc/Lambda

Bohr's Theory of the Hydrogen Atom

- Electrons can only occupy certain discrete energy levels in atoms.

- The atom does not radiate energy while in one of its stationary states (orbits).

- Electrons absorb or emit energy in discrete amounts (photons) as they move from one energy level to another.

- E absorbed = E emitted

Conclusion: Electrons revolve around the nucleus of an atom in specific "orbits."

Continuous Line Spectra

contains all wavelengths of visible light

Line Spectrum

contains only specific wavelengths of visible light that are characteristic of the species producing them

Atomic Spectra

discontinuous

J.R Rydberg

Studied the H lines and found that their wavelengths followed a specific equation

Energy Series

Lyman - 1 - 2,3,4 - UV

Balmer - 2 - 3,4,5 - Visible and UV

Paschen - 3 - 4,5,6 - Infrared

Brackett - 4 - 5,6,7 - Infrared

Limitations of the Bohr model

works well for any one-electron species but fails to predict the spectrum of any other atom

Louis de Broglie

- If light waves can behave like a stream of particles (photons), then perhaps particles such as electrons can possess wave properties.

- If electrons have wavelike motion and are restricted to orbits of fixed radii (as Bohr proposed), that would explain why they have only certain possible frequencies and energies

Wave-Particle Duality of Matter and Energy

λ = h/mc (de Broglie Equation)

matter behaves as though it moves in a wave

Heisenberg Uncertainty Principle

- It is impossible to determine accurately both the momentum (mass and velocity) and the position of an electron simultaneously.

- Electrons are not in orbit around the nucleus in the true sense of the word.

- Electrons only have a probability of being located within a specified region of space.

Postulates of Quantum Mechanics

- Atoms and molecules can exist only in certain energy states.

- When atoms or molecules absorb or emit EMR, they change their energies.

- The allowed energy states of electrons in atoms and molecules can be described by sets of numbers called quantum numbers.

Quantum Numbers

Each electron is identified by a set of 4 quantum numbers.

- Principal Quantum Number

- Angular Momentum Quantum Number

- Magnetic Quantum Number

- Spin Quantum Number

Principle Q.N

Symbol: n

Determines how far the electron is from the nucleus.

n = 1, 2, 3, 4, 5, 6, 7, ...

Angular Momentum Q.N

Symbol: l

Determines the shape of the volume of space (orbital) that the electron can occupy.

Each l corresponds to a sublevel: 0 = s, 1 = p, 2 = d, 3 = f

Magnetic Q.N

Symbol: ml

Determines the orientation in space of the volume (orbital) that can contain the electron.

Each subshell contains orbitals.

Each orbital is associated with an ml .

For each l, ml = - l, ..., 0, ..., + l

Spin Q.N

Symbol: ms

Electron Spin

Indicates the direction that the electron is spinning on its axis.

ms = +½ or -½ for each combination of ml and l

Shapes of Orbitals

s = spherical

p = dumbell

d = flower or complex

f = complex

Aufbau Principle

electrons enter orbitals of lowest energy first.

n + l Rule

- orbitals increase in energy as the sum n + l increases.

- If two orbitals have the same value of n + l, then the one with the lower n value is lower in energy.

Pauli Exclusion Principle

- No 2 e- in an atom can have the same set of 4 Q. N.

- Each orbital can contain at most 2 e- with opposite spins.

Hund's Rule

- When electrons occupy orbitals of equal energy (such as three p orbitals), one electron enters each orbital until all the orbitals contain one electron with the same spin.

- Second electrons then add to each orbital so that their spins are opposite that of the first electron in the orbital.

Paramagnetic

Atoms with unpaired electrons are attracted to a magnetic field

Diamagnetic

Atoms with no unpaired electrons are repelled by a magnetic field