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 10 8 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 light E = h (where h is Planck’s constant, 6.63x 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 = -(R H ) / (n 2 ) where R H = x 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, m l : Distinguishes orbitals of same shape but different position (m l = integers from – l to + l) Spin quantum number, m s : 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 nlmlml Notation# orbitals 1001s1 2002s1 21-1, 0, +12p3 3003s1 31-1, 0, +13p3 32-2, -1, 0, +1, +23d5

Atomic orbital shapes