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.