Chapter 7: The quantum-mechanical model of the atom

The nature of light Light – electromagnetic radiation that is composed of oscillating electric and magnetic fields which are perpendicular to each other Magnetic field – a region in space where a magnetic particle will experience a force electric field – a region in space where an electrically charged particle will experience a force Light travels at the speed of….. light! 3.00 x 108 m/s The letter “c” can be used to stand for light Wave-particle duality – light can behave as a particle and a wave

Light’s wave nature A wave oscillates, giving an amplitude and a wavelength amplitude – the vertical height of a crest in the wave wavelength (λ)– the length of the wave Visible light has a wavelength between 400-750nm Frequency (v) – the number of cycles of a wave that pass through a stationary point in a given time period Units of frequency = hertz = Hz = cycles/second = 1/s = s-1

The electromagnetic spectrum Electromagnetic spectrum – gives ranges of types of electromagnetic radiation based on wavelength or frequency or energy Radio – microwave – infrared – visible light – ultraviolet – X-ray – gamma ray

Practice What is the wavelength of a beam of light that has a frequency of 4.62 x 1014 Hz c = 3 x 108 m/s v = 4.62 x 1014 Hz What type of electromagnetic radiation is this?

Wave interference Waves can interact with other waves through interference Depending on the degree of interference, waves can produce constructive or destructive interference

Diffraction Diffraction – when a wave bends around an obstacle or slit Slit must have comparable size to the wavelength This is different than how a particle would behave

Diffraction patterns

Light’s particle nature photo electric effect – when a metal emits electrons after light shines upon them Light energy comes in discrete packets Photon or quantum of light – a packet of light Each photon has an associated energy dependent on its frequency (v) h = Planck’s constant = 6.62 x 10-34 (J*s)

Photoelectric effect continued For a photon of light to be able to kick out an electron off of a metal, it must have at least a certain amount of energy, it must pass a certain threshold φ = Binding energy of an emitted electron All excess energy over the threshold turns into kinetic energy of the electron

Practice A nitrogen gas laser pulse with a wavelength of 337 nm contains 3.83 mJ of energy. How many photons does the pulse contain? Can a photon from this type of light excite an electron from Aluminum, which has a threshold energy of 6.88 x 10-19J?

Atomic spectroscopy When an atom absorbs energy it can reemit that energy as light Depending on the atom, different colors can be emitted Although one color may be perceived, an emission spectrum is produced

Sodium Potassium Lithium Barium

Bohr Model Niels Bohr (1885-1962) proposed that electrons orbit the nucleus at different energy levels An emission spectrum that is produced is derived from electron energy level transitions

Hydrogen electronic transitions The energy of an electron in an energy level (n) is represented from the equation below Higher n value = less negative energy = higher energy En is negative because the electrons energy is lowered by its interaction with the positively charged nucleus As n increases, the rate at which the energy increases is less The difference in energy between the n =2 and n = 3 is less than the difference between n = 1 and n = 2

If an electron jumps from one energy level to another, the change in energy can be calculated nf = final energy level ni = initial energy level

Determine the wavelength of light emitted when an electron in a hydrogen atom makes a transition from an n = 6 to n = 5 energy level.

The wave properties of matter Electrons can also display wave properties Can also produce diffraction patterns from two closely spaced slits

The de Broglie wavelength Since we can describe electrons as having wave properties, we can utilize wave equations to describe electrons h = planck’s constant 6.626 (kg*m2)/(s2) m = mass of electron 6.626 x 10-31 kg v = velocity of electron in m/s If you know the velocity of an electron, you its wavelength

Schrödinger’s cat An electron can exhibit wave and particles properties (wave-particle duality) It can exist in two states at the same time, but upon observation, one state is observed Erwin Schrödinger (1887-1961) proposed a thought experiment where a sealed box contains a cat, a radioactive atom, and a device that will kill the cat if the radioactive atom emits a particle upon radioactive decay The radioactive atom exists in both the emitted and non emitted states, making the cat both dead and alive

The uncertainty principle Although electrons can exist as waves and particles, observation forces it into one state, excluding the other state Complementary properties – properties that exclude each other, the more we know one the less we know the other Position and velocity of an electron are also complementary properties Werner Heisenberg’s (1901-1976) formulized Heisenberg’s uncertainty principle Δx = uncertainty in position Δv = uncertainty in velocity

Indeterminacy For macroscale objects Newton’s laws of motion are useful and position and velocity can both be known simultaneously, and also considered deterministic Deterministic – the present determines the future For electrons the position and velocity are not known, so its future is uncertain Indeterminacy – the future path can not be precisely determined A probability map is more effective at determining the future of the electron

Atomic orbitals Orbital – a probability distribution map of where an electron is likely to be found A house for the electrons Though position is uncertain, the energy of the orbital is Quantum numbers specify properties of a orbital and an electron that may reside inside of it n, l, ml, ms

Principal quantum number (n) n – determine the size and energy of an orbital The value of n is an integer n = 1,2,3,... and so on En = energy for an electron in a hydrogen orbital

Angular momentum quantum number (l) l – determines the shape of an orbital The value of l can range be 0,1,2,3,… (n – 1) The value of n determine the possible l values If n = 2, l can be 0 or 1 l can also be represented with letters to avoid confusion

Magnetic quantum number (ml) ml - an integer that specifies the orientation of the orbital Possible values determined by the l value -l to +l l = 2, then ml can be -2, -1, 0, +1, +2

Spin quantum number (ms) Electrons are considered to have a spin Due to a electrical particle spinning it also creates a magnetic field ms – refers to the orientation of the spin of the electron in an orbital ms = +1/2 = spin up ms = -1/2 = spin down

The shapes of atomic orbitals The angular momentum quantum number (l) defines the type/shape of an orbital A probability density represents an orbital, being the region where an electron can exist in an atom A radial distribution function shows the probability of finding an electron within a thin spherical shell at a distance r from the nucleus Probability density for an 1s orbital

s orbitals (l = 0) When l = 0, you have an s orbital which is has a spherical shape Depending on the principle quantum number you will have a smaller or larger s orbital n = 1 , l = 0  1s orbital n = 2 , l = 0  2s orbital n = 3 , l = 0  3s orbital Since l = 0, and the formula for ml = -l to +l, ml = 0 There is only one s orbital per principle level

p orbitals (l = 1) When l = 1, you have an p orbital which is has a dumbbell shape n = 1 , l = 1  1p orbital DOESN’T EXIST n = 2 , l = 1  2p orbital Since l = 1, and the formula for ml = -l to +l, ml = -1, 0, +1 There are three p orbitals per principle level ml = -1  px ml = 0 py ml = +1 pz

d orbitals (l = 2) When n = 3 or greater and l = 2, you have an d orbitals Since l = 2, ml = -2,-1, 0, +1, +2 There are five d orbitals per principle level

f orbitals (l = 3) When n = 4 or greater and l = 3, you have an f orbitals Since l = 3, ml = -3, -2,-1, 0, +1, +2, +3 There are seven f orbitals per principle level

Practice If n = 4, which of the following values for l are not allowed? 1, 3, 4, 7 If l = 3, what is the correct ml values allowed? A. -1, 0, +1 B. 0, 1, 2, 3 C. -2, -1, 0, +1, +2 D. -3, -2, -1, 0, +1, +2, +3 Which type of orbital is represented by the previous l value?

The overall shape of an atom Most atoms have many electrons that fill up many orbitals The overall shape of the atom is a collection of all those orbitals s, p, d, f, n= 1,2,3,4,… The overall shape is like a sphere

Schrödinger’s Chapter 7 (finished/not finished)