Chapter 4 - The structure of atoms

What kind of wave is light?

An electromagnetic wave

Visible light and color

For visible light, wavelength determines color. The visible spectrum runs from wavelengths of about 400nm to roughly 750 nm (from violet to red)

Where does light come from

Photons

Wave particle duality

The idea that light sometimes behaves as a waves and at other times like a particle. Which behavior is observed depends on the particular experiment.

When is a photon released?

When an electron jumps from one allowed orbit to another. When it goes up it absorbs energy and when it jumps down it releases energy and releases a photon that emits a light.

What is the energy that is found in a system where the electron orbits around the nucleus?

The energy of such a system is the sum of kinetic and potential energy.

• The kinetic energy follows from the speed of the orbiting electron

• The potential energy originates from electrical coulomb interactions between nucleus and electron.

Formula for energy in orbital

• R_H is called the Rydberg constant

• n is the quantum number (the orbit number)

• R_Hhc in total has a number of 2.18 × 10^-18 J

• This formula states that the energy of an hydrogen atom only can take specific values.

• ONLY WORKS FOR HYDROGEN

Limitation Bohr model

Only works for atoms with one electron

Formula Bohr for charged one electron atoms

• Z is the atomic number which is equal to the number of protons in the nucleus.

Motion of electrons

waves

Correct equation after Bohr’s equation

• H stand for the Hamiltonian operator, a set of mathematical operations that represent the total energy (kinetic and potential) of the electron

• E stands for the actual energy of the electron.

• The symbol v is the wave function that represents the standing wave form of the electrons.

What does quantum mechanics say about where electrons are

Quantum mechanics tells us that it is impossible to know precisely where an electron is and where it travels.

• We can only know the probability for an electron to be somewhere.

Wavefunction ψ

• The wave function (v) tells us something about the probability for an electron to be somewhere

• The square of the wave function tells us the probability density, that is the probability per unit volume for an electron to be at a certain location.

Quantum numbers

These numbers determine the shape of the standing wave in a vibrating string. Since the orbitals are standing waves in three dimensions we need three quantum numbers to fully describe them.

The three types of quantum numbers

1. The principle quantum number

2. The angular momentum quantum number

3. The magnetic quantum number

The principle quantum number

• Positive integer

• Related to the size and energy of the orbital

• As n increases, the orbital becomes larger and the electrons spends more time farther away from the nucleus.

• Therefore the energy of the electron also increases with increasing n, because the attraction to the nucleus is weaker.

The angular momentum quantum number

• An integer that can take values from 0 to n-1

• This quantum number is related to the shape of the atomic orbitals

• Each value of l is also assigned a letter: l = 0 = s orbital

• l = 1 = p orbital

• l = 2 = d orbital

• l = 3 = f orbital

The magnetic quantum number

• -I, …, +I

• Orientation in space

The photoelectric effect

• When you shoot a specific wavelength on a sheet of metal than it will release energy

• When you decrease wavelength (higher frequency) the electron emitted has more energy

Line spectra formula

• n1 < n2

• final < initial

wavelength fromula

wavelength = c/v

v= frequency

Formula Broglie

wavelength = h/mv

• V IS NOT FREQUENCY HERE BUT VELOCITY IN (M S-1)

what is ionization

movement of electron up an orbital