-The Bohr Model -The Quantum Mechanical Model Warner SCH4U Chemistry

-The Bohr Model-The Quantum Mechanical Model

Warner SCH4U Chemistry

Dalton’s Atomic Model

Plum Pudding Model (Thomson)

Niels Bohr (Born in Denmark 1885-1962) Student of Rutherford Through his study of

light, Bohr came up with a theory of how electrons were arranged within an atom.

What is Light?

Light: Electromagnetic radiation that travels through space or matter in wave like oscillations.

Sometimes we refer to it as a wave and sometimes we refer to it as a particle (photon)

Photon

Bundles (package) of light energy

Characteristics of Light – frequency, wavelength, energy

Max Planck (1858-1947)

Planck proposed that photons of light carry energy and devised E=h

E=energy

=frequency

h=Planck’s constant 6.7x10-34Js

A quantum is the Latin word for discrete amount of energy

Quantum – term first used by Planck

Niels Bohr’s Model (1913)

Based on his study of light he stated that electrons orbit the nucleus in circular paths of fixed energy (energy levels).

Niels Bohr’s Atom Cont’d

Electrons can jump from energy level to energy level.

Electrons absorb or emit light energy when they jump from one energy level to another.

Quantum jump is amount of energy required to move an electron from one energy level to another.

Excited State and Ground State

Ground state: the lowest possible energy level an electron be at.

Excited state: an energy level higher than the ground state.

Colour of light

Each electron that jumps back emits one photon of light

What colour is this light? Depends on how big the jump between

orbits was The bigger the jump, the higher the energy.

Energy

Energy of Emitted Photon

Energy of the emitted photon =

Difference in energy between two states

Energy emitted by the electron as it falls back from the higher to the lower energy level is proportional to the frequency of the light wave.

The energy levels are like the rungs of a ladder but are not equally spaced.

Excited states are unstable. Electrons quickly falls back to the ground state, but not always in a single step. For example, if the electron is initially promoted to the n=3 state, it can decay either to the ground state or to the n=2 state, which then decays to n=1.

Emission Spectrum

Light emitted produces a unique emission spectrum.

Hydrogen Emission Spectrum

Violet

Blue

Red

Balmer Series

Colour seen is a result of different wavelengths of light (colours) emitted when the electrons go down the step(s) to their ground state.

Each element will have its own set of steps, therefore each will have its own colour.

Some colours are very similar so a more exact method can be used to identify the elements.

Flame Test Colour

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Bohr Model for Hydrogen

The Bohr model explained the emission spectrum of the hydrogen atom but did not always explain those of other elements.

Quantum Mechanical Model

1920’s Werner Heisenberg (Uncertainty Principle) Louis de Broglie (electron has wave

properties) Erwin Schrodinger (mathematical equations

using probability, quantum numbers)

Werner Heisenberg: Uncertainty Principle

We can not know both the position and momentum of a particle at a given time.

The Wave Model

Uncertainty Principle makes it impossible to plot an orbit for an electron. Is this a problem? NOThe probable location of an electron is based on how much energy the electron has.

Louis de Broglie, (France, 1892-1987)Wave Properties of Matter (1923)

Since light waves have a particle behavior (as shown by Einstein in the Photoelectric Effect), then particles could have a wave behavior.de Broglie wavelength

h mv

Electron Motion Around Atom Shown as a de Broglie Wave

What is an electron? https://www.youtube.com/watch?v=O55XiriEaQI#t=11

1. The electron was treated as a wave 2. Light was treated as a particle (photon)

What is an electron? Is it a particle or a wave? And what is light? A wave or a photon?

The Electrons: wave or particle Electrons display properties of both. To think of them as a particle is easy because

they have a small amount of mass. There is evidence of wave behavior though. In this sense they are neither particles nor

waves in the absolute sense, but only exhibit wave or particle properties, depending on the experiment being performed.

Erwin Schrodinger, 1925Quantum (wave) Mechanical Model of the Atom

Four quantum numbers are required to describe the state of the hydrogen atom.

FYI: Schrodinger’s Equations!!!

is called the wave function and indicates the probability of where an electron may be found.

According to the modern atomic model, an atom has a small positively charged nucleus surrounded by a large region in which there are enough electrons to make an atom neutral.

We can plot the position of an electron over and over again and gradually build a 3D map of the places that the electron is likely to be.

These defined regions are called orbitals

Atomic Orbital:

A region in space in which there is high probability of finding an electron.

Electrons whirl about the nucleus billions of times in one second

They are moving around in random patterns.

Location of electrons depends upon how much energy the electron has.

Quantum-Mechanical Model

Electron Orbital:

Depending on their energy, electrons are locked into a certain area in the cloud.

Electrons with the lowest energy are found in the energy level closest to the nucleus

Electrons with the highest energy are found in the outermost energy levels, farther from the nucleus.

The Electron Cloud

The electron cloud represents positions where there is probability of finding an electron.

The Electron Cloud

http://www.chemeng.uiuc.edu/~alkgrp/mo/gk12/quantum/H_S_orbital.jpg

The higher the electron density, the higher the probability that an electron may be found in that region.

Quantum Mechanical Model

Electrons are located in specific energy levels.

There is no exact path around the nucleus.

The model estimates the probability of finding an electron in a certain position.

Quantum Numbers:

specify the properties of atomic orbitals and their electrons.

Four Quantum Numbers

1. Principal Quantum Number

2. Orbital Quantum Number

3. Magnetic Quantum Number

4. Spin Quantum Number

Principal Quantum Number, n

Indicates main energy levelsn = 1, 2, 3, 4…

Each main energy level has sub-levels

The maximum number of electrons in a principal energy level is given by:

Max # electrons = 2n2

n= the principal quantum number

Orbital Quantum Number, ℓ(Angular Momentum Quantum Number)

Indicates shape of orbital sublevels ℓ = n-1

ℓ sublevel0 s

1 p

2 d

3 f

4 g

Atomic Orbital s

2s

The 3 p orbitals

http://www.rmutphysics.com/CHARUD/scibook/crystal-structure/porbital.gif

The d orbitals

f orbitals

Magnetic Quantum Number, ml Indicates the orientation of the orbital in space. Values of ml : integers -l to l The number of values represents the

number of orbitals. Example: for l= 2, ml = -2, -1, 0, +1, +2

Which sublevel does this represent?Answer: d

Electron Spin Quantum Number, (ms or s)

Indicates the spin of the electron (clockwise or counterclockwise).

Values of ms: +1/2, -1/2

Example:

List the values of the four quantum numbers for orbitals in the 3d sublevel.

Answer:

n=3

l = 2ml = -2,-1, 0, +1, +2

ms = +1/2, -1/2 for each pair of electrons