Atomic Structure & properties 3
Louis de broglie added to wave-particle duality
All matter possess a wavelength
magnetic quantum number (m)
Indicates the orientation of the orbital around a nucleus. Each new sublevel has a larger amount of orientations
Wavelength is inversely proportional to what?
Mass and velocity
the wavefunction is solved on the basis of energy of the particle using the
SWE
wave particle duality of electron
particle property Einstein E=mc^2 Wave property Planck E=hv therefore λ = h/p = h/mu
if 2 electrons are parallel they have ___ ___
same spin
Principal quantum number (n) 1,2,3,4
Indicates distance from nucleus. The smaller the number, the closer the electron is to the nucleus. Corresponds with energy levels of atoms. as n increases, electrons at higher energy level further from nucleus n determines the size and energy (to remember: "n" stands for "number" because it's written as a number)
Spin quantum number (s)
Indicates the difference between a pair of electrons. Electrons can either have spin 1/2 or -1/2 (Up or Down) Each orientation (orbital) can hold a pair of electrons, which are represented by arrows. s - 1 orientation - 2 electrons p - 3 orientations - 6 electrons d - 5 orientations - 10 electrons f - 7 orientations - 14 electrons
Angular Momentum quantum number (l)
Indicates the shape (sublevel) of the orbital that the atom is on. (angular distribution of the orbital) Takes integer values from 0 to n-1
A wave function
A MATHEMATICAL FUNCTION that contains detailed information about the behaviour of an electron. an atomic wavefunction consists of a radial component and angular component the region of space define by a wave function is called an atomic orbital Mathematical function that varies with position
the 2 types of nodes
Agular nodes (l) and radial node (n-1-l) angular node is a planar or conical surface a radial node is a spherical surface surrounding the nucleus
how does the uncertainty principle highlight the inadequacy of the bohr model
Bohr's model of the atom assumes fixed orbits AND trajectories for the electron. Simultaneously known orbits and trajectories violate the Heisenberg Uncertainty Principle. The problem is, electrons do NOT travel in fixed orbits, and they do NOT travel with fixed trajectories. That is, they should NOT have simultaneously well-known positions x and momenta p
viewing 3-dimensional wave function shows us why
electron position is so uncertain
wave-particle duality
electrons and light can behave as both a wave and particle wave like properties: -associated wavelengths, frequency and energy -diffraction of e- particle like properties: -photons-energy associated with mass & momentum -photoelectric effect
electron properties
electrons observed as light (cathode ray tube experiment) electrons has mass (Millikan's experiment)
orbitals are described by designated quantum numbers (n,l,m) which define the
energy, shape and spacial orientation
does knowing the electron travel in a waveform having an associated energy allow us to determine its location?
no
if 2 electrons are paired they have ___ ___
opposite spin
Electrons jump between ________ like particles
orbitals
all matter has a wavelength associated with it and very small objects such as electrons behaviour either as
particles or waves
both position and momentum cannot be determined ________
precisely simultaneously
wave function has radial and angular components and describes
regions of space where electrons are moving
describing the location of an electron if there are different locations of the electron leading to different orbitals what would make orbitals different from each other?
size- different energy based on how far electron is from nucleus shape- what is the specific region of space the electron is moving in orientation- in what direction (what angle) above the nucleus is electron moving quantum numbers define the type of orbital
every shell can be divided into _______ of electron pairs
sub orbitals
What does quantum theory define?
the allowed energy of electrons using 4 quantum numbers
Quantum mechanics is
the branch of physics that describes electron's position within an atom (which we don't really know but can predict the probability)
There are 2 Schrodinger equation problems:
the particle in a box and the H atom
uncertainty principle also called Heisenberg uncertainty principle or indeterminacy principle, statement, articulated (1927) by the German physicist Werner Heisenberg, states that
the position (x) and the momentum (p) of an object cannot both be measured exactly, at the same time, even in theory at high speed-freeze motion location is preciously known but direction and speed is uncertain at low speed- blur is seen location is uncertain but direction and motion are certain
square of wavefunction = electron probability density which describes
the probability of finding electron in a specified region of space
De BROGILE WAVE EQUATION
λ = h/p = h/mu describes wave and particle nature of small particles such as electrons
Electrons is a what kind of wave?
Circular standing wave
Deriving the de Broglie Wavelength
De Broglie first used Einstein's famous equation relating matter and energy E=mc^2 with E = energy, m = mass, c = speed of light sing Planck's theory which states every quantum of a wave has a discrete amount of energy given by Planck's equation: E=hν with E = energy, h = Plank's constant (6.62607 x 10-34 J s), ν= frequency Since de Broglie believed particles and wave have the same traits, he hypothesized that the two energies would be equal: hv=mc^2
What are quantum numbers used for?
They are used to show the location of an electron in an atom. Like an atom's address or coordinates.
Assuming that matter (e.g., electrons) could be regarded as both particles and waves, in 1926 Erwin Schrödinger formulated
a wave equation that accurately calculated the energy levels of electrons in atoms. The Schrödinger's equation describes the behaviour of a system by a wave equation.
standing wave, also called stationary wave, combination of two waves moving in opposite directions, each having the same
amplitude and frequency. The phenomenon is the result of interference; that is, when waves are superimposed, their energies are either added together or canceled out. In the case of waves moving in the same direction, interference produces a traveling wave. For oppositely moving waves, interference produces an oscillating wave fixed in space.
Schrodinger described the wave motion of
an electron moving within a confined space as a wave function it is quantized and 3 dimensional motion
proof of diffraction of electrons
beam of electrons diffracted by a crystal diffraction is a property of light only
what information does the wave function provide about the electron
describe the wave motion of the electron has an associated principle quantum number, n electron found in a defined region of space
Schrodinger wave equation (SWE) solves
the wavefunction for the electron in the atom and relates it to energy of the electron for a particular distance from the nucleus wave equation in terms of the wavelength which predicts precisely the probability of locating the electron it solves for the wavefunction for the electron in the atom and relates it to energy of the electron for a particular distance from the nucleus
the HUP states that it is impossible to know both the precise position and momentum of an object simultaneously. how does this relate to electrons?
this uncertainty cannot be ignored for atoms and subatomic particles such as electrons the electrons position cannot be known with great certainty
development of quantum mechanics
wave particle duality uncertainty principle
electron motion is described by the
wavefunction
Schrödinger explained that electrons move in terms of
waves and not in particle leaps.