The Quantum Model Part II Energy as wave and particle.

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-)