# The Quantum Model Part II

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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 NOT spherical for other orbitals. Nodal surfaces are spherical for the “s” orbitals. 2p orbital 3s orbital

The Electromagnetic Spectrum

What is light? Wave Particle

How many wavelengths are represented in each figure below?
Waves: A Warm up

Wave Comparison Red Light Low frequency Long wavelength Violet Light
nm = 1 x 10-9 m Red Light Low frequency Long wavelength Violet Light High frequency Short wavelength

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:

Principle Energy Level (n)
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 Energy Level (n) Ratio of Level 1:Level X -2.18E-18 1 -5.45E-19 2 4 E-19 3 9 E-19 16 -8.72E-20 5 25 E-20 6 36 E-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 de Broglie Bohr to

de Broglie and Wave Model
An electron in its path is associated with a wavelength. The wavelength depends on the mass:

Example Problem What is the characteristic wavelength of an electron with a velocity of 5.97 x 106 m/s? (Use 9.11 x kg for the mass of an e-)