The Quantum Model Part II Energy as wave and particle
Mar 27, 2015
The Quantum Model Part II
Energy as wave and particle
Shapes of s orbitals
s orbital
s orbitals
Shapes p orbitals
Nodal plane
Shapes of d orbitals
Heisenberg Uncertainty Principle An electron’s location and speed cannot be
determined at the same time. If we cause change to find one variable, we are no
longer looking at the actual e- situation. If we need to slow or stop it to locate it or if we need to
locate it to find its speed, then we allow the chance of change.
So quantum mechanics can tell us the probability that an electron is somewhere, but it does not tell us how it got there.
Nodal Surfaces A nodal surface is a region that defines the border of an
orbital. This is where the probability function equals zero. Electrons CAN NOT exist in this area.
Nodal surfaces are spherical for the “s” orbitals.
3s orbital
Nodal surfaces are NOT spherical for other orbitals.
2p orbital
The Electromagnetic Spectrum
What is light? Wave
Particle
Waves: A Warm up
How many wavelengths are represented in each figure below?
Red Light
Violet Light
• Low frequency
• Long wavelength
• High frequency
•Short wavelength
Wave Comparisonnm = 1 x 10-9 m
c =
It stands to reason that if energy is constant then (wavelength) is inversely proportional to (frequency).
OR
As wavelength increases frequency decreases
Example Problem Refer to #1 on your Worksheet.
Max Planck
• Max Planck mathematically determined “h” that could be multiplied by to solve for energy (E) every time an electron gave off light as it fell. (This simply means that all wavelengths are proportional)
E = h
Pink Floyd
Photoelectric Effect
Bohr Model Bohr was able to calculate the energy for the
allowed orbits of the hydrogen atom using the formula:
Since this is true of any level, Bohr postulated the energy between energy levels could be calculated as well:
Bohr Model Emission Spectra
explains Hydrogen
Electrons exist in quantized energy levels
As electrons ‘drop’ to lower energy levels emitting quanta of energy which translate to frequencies
& wavelengths
Energy (Joules)
Principle Energ
y Level
(n)
Ratio of
Level 1:Level
X
-2.18E-18 1 1
-5.45E-19 2 4
-2.42222E-19 3 9
-1.3625E-19 4 16
-8.72E-20 5 25
-6.05556E-20 6 36
-4.44898E-20 7 49
Energy of Electrons We can calculate the energy the electrons of a hydrogen atom
emits when they fall by using the Balmer equation
So if an electron falls from the 3rd energy level to the 2nd energy level then –
Note: energy levels are not actually distances between electrons and the nucleus.
Excited atoms
Spectral Lines
Photons of different energies are released as electrons return from different energy levels.
When electrons return to the second energy level, it is visible light Balmer Series
Some Atomic Emission Spectra Hydrogen
Mercury
Argon
Helium
Hydrogen Emission Spectrum
Bright-line Spectra Atoms are quantized, existing only in definite energy states
when an atom absorbs a specific quanta of energy electrons jump to higher energy levels.
An “EXCITED” electron jumps from its ground state to a higher energy level.
The energy cannot be maintained so it falls back to where it came from losing exactly the same amount of energy that it absorbed.
De Broglie Small matter (electrons) have wavelike properties as
well.
Changed the Bohr model so that all elements could be explained according to their frequencies of energy.
Remember that energy is constant and that standing waves are quantized as well (they only increase by multiples of ½)
De Broglie
Essentially the model went from
Bohr
to
de Broglie
de Broglie and Wave Model An electron in its path
is associated with a wavelength.
The wavelength depends on the mass:
Example ProblemWhat is the characteristic wavelength of an electron with a velocity of 5.97 x 106 m/s? (Use 9.11 x 10-31 kg for the mass of an e-)