Chapter 7: Quantum theory of the

atom

Chemistry 1061: Principles of Chemistry I

Andy Aspaas, Instructor

Atomic emission and line spectra

• When different compounds are burned, they give off surprisingly different colors of light

– It can be used to identify certain compounds

• If the emitted light is sent through a prism so the colors are separated, only certain discrete colors of light are given off (atomic line spectrum)

• The color of light can be related to the amount of energy that light contains

The wave nature of light

• Electromagnetic radiation: energy that is in the form of a wave, (visible light, x-rays, radio waves, etc)

• Wavelength, : distance between any two adjacent identical points of a wave

– Visible light, wavelength measured in nm– Radio waves can be measured in m

• Frequency, (nu): number of wavelengths that pass a fixed point in one unit of time (usu. 1 second)

Electromagnetic spectrum

Frequency and wavelength

• All electromagnetic waves travel at the speed of light, c = 3.00 x 108 m/s

• c = , if is in m, and is in sec-1

– Visible light wavelengths are always given in nm, between 400 and 800 nm

– Frequency is usually given in sec-1, or Hz

The particle nature of light

• While light has wave-like properties, it also has particle-like properties

• Photon: discreet particles of energy which make up light (or any electromagnetic radiation)

• The energy of one photon of light is related to the frequency of that lightE = h • (where h is Planck’s constant, 6.63x10-34 J·s)• This relates the wave-like and particle-like

properties of light

More about atomic line spectra

• Heated solid metals emit light of all wavelengths, or a continuous spectrum

– Would form a rainbow if sent through a prism

• Heated gases emit light of only particular wavelengths, or a line spectrum

– Would form only lines of particular colors if sent through a prism

– These lines are associated with energy level transitions

Energy levels

• Electrons can have only specific energy values in an atom (energy levels)

– Energy levels are quantized (only specific allowed values)

• When an electron absorbs energy from the environment, it can be promoted to a higher energy level

• In order for it to return to a lower level, energy must be released in the form of a single photon

– Depending on which levels this transition involves, the photon will have a different amount of energy

H atom energy level calculations

• Energy levels are numbered with integers starting with 1, symbol is n

n = 1, 2, 3, …• The energy of a particular level is given by

E = -(RH) / (n2) where RH = 2.179 x 10-18 J

• The energy of a photon given off can be calculated by subtracting the lower energy level from the higher energy level (energy of a photon is positive)

Quantum mechanics

• Just like light can be wave-like and particle-like, so can electrons

• The most accurate description of an electron’s behavior is using a wave-like interpretation, this is known as quantum mechanics

• An electron can be described by a wavefunction – an equation for the wave that represents an electron

• Only the probability of an electron appearing in a certain place can be calculated

– Heisenberg uncertainty principle says the more precisely you know the position of a small particle, the less precisely you know its momentum

Atomic orbitals

• The 3-dimensional space in which there is a high probability of finding an electron in an atom is referred to as an atomic orbital

• Can be described by three quantum numbers

– Principal quantum number, n: refers to the energy of an electron, it also associates with the size of an orbital (n = 1, 2, 3, 4,…)

Atomic orbitals

• Angular momentum quantum number, l: indicates shape of orbital (l = 0, 1, 2, 3, …. n-1)

– Usually shown by letters: s, p, d, f, and g

• Magnetic quantum number, ml: Distinguishes orbitals of same shape but different position (ml = integers from –l to +l)

• Spin quantum number, ms: indicates which of 2 possible spin states an electron is in, equal to either -1/2 or +1/2

Permissible atomic orbitals for n = 1, 2, 3

n l mlNotation # orbitals

1 0 0 1s 1

2 0 0 2s 1

2 1 -1, 0, +1 2p 3

3 0 0 3s 1

3 1 -1, 0, +1 3p 3

3 2 -2, -1, 0, +1, +2 3d 5

Atomic orbital shapes