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Quantum Mechanics (Grade 12)
Transcript of Quantum Mechanics (Grade 12)
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12.2: The Quantum Idea
Max Plank & Energy Waves
A black body is refers to any non-transparent object that emits thermal radiation.
The ideal black body is one that absorbs all incoming light and does not reflect any.
At room temperature the object would be completely black, and when heated to higher temperatures the black body would begin to glow.
Wednesday, June 11, 2014
Vol XCIII, No. 311
Flaws of the Wave Theory
Introduction to Quantum Mechanics
1. According to the wave theory, a system's energy could be any value but this was proved incorrect. From several experiments, scientists observed that atoms & electrons have very specific & consistent energy values.
2. Light has exhibited several unusual properties (ex. momentum) that the wave theory couldn't explain (b/c according to the theory, waves can't have a mass).
3. Electrons, protons and neutrons are particles & considering the wave theory, they should not have wave characteristics. (Even so, all 3 particles have been defracted in experiments.)
4. Electrons orbiting an atom should lose energy due to electromagnetic radiation & fall into the nucleus but this doesn't occur.
12.5: De Broglie & Matter Waves
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12.3: The Photoelectric Effect
Compton Effect- Light has momentum!
12.4: Momentum & Photons
12.6: The Bohr Atom & 12.7: Probability Waves
So far, in Physics we've learned the ideas of matter & energy separately and that both can't be created or destroyed. The Quantum Theory (AKA "quantum" or "wave mechanics") is the theory of how atoms, matter and energy relate to each other.
In mechanical waves increasing the amplitude of a wave, increases the amount of energy transferred. So..Is the same true for light?
Light is made up of electromagnetic waves.
Which kind of lights have more energy? The more intense ones.
Sunburns and welding arc penetrate through skin. But bright stage lights do not.
The amount of energy transferred in lights (electromagnetic waves) does not increase with amplitude but with content. Ex. UV radiation
Planck- Suggested that light travels in packets called quanta.
Planck suggested that the smallest possible packet that can be associated with a given wavelength is given by the equation.
Eγ = hf
E = The energy of a given quantum in joules (J)
h = Planck’s constant = 6.626x10 -34 J∙s
f = The frequency of the light in hertz (Hz or s-1)
The Energy of a system can be of any value. Energy can travel in two forms of waves: electromagnetic and mechanical Waves.
Electromagnetic Waves: Waves that can transmit energy through a vacuum (ex. Empty space) – does not require a medium.
Examples: Light, TV, Microwaves
Mechanical waves: Waves that is not capable of transmitting energy through a vacuum - requires a medium.
Examples: Ocean and Sound Waves
This equation gives the quantum energy that can be transferred for a given wavelength of electromagnetic radiation
With substituting the wave equation into Planck’s equation we get a new equation for QUANTUM ENERGY!
Wien's (displacement) Law tells us that objects of different temperatures emit spectra that peak at different wave lengths, therefore:
Hotter objects emit most of their radiation at shorter wavelengths – Appear Bluer
Cooler objects emit most of their radiation at longer wavelengths – Appear Redder.
12.8: Heisenberg's Uncertainty Principle
The Uncertainty Principle:
If we know the position of a particle, we cannot know its momentum and vice versa. Similarly, if we know the energy of a particle, we cannot know the length of time it has energy and vice versa. (pg. 620)
Eγ = hf
Wave Equation: C = fλ (Rearrange) f = c/λ
Eγ = hc
Ionization Energy & Wave Particle Duality of Light
• If one or more electron groups are lone pairs, the molecular shape is not given the same name as its electron group arrangement.
• These types of molecules have 3 repulsive forces: Between bonding pairs (BP-BP), between lone pairs (LP-LP) and between a bonding pair and a lone pair (BP-LP).
*According to the VSEPR model, repulsive forces decrease: LP-LP > BP-LP > BP-BP.
• Lone pairs take up more space than bonding pairs because they spread out more. Due to this, lone pairs exert a strong repulsive force on neighboring lone pairs and bonding pairs
Refer to page 618 & 619 of your textbook
1:10 A.M. and I am still awake...
Blah, blah, blah...
12.9: Quantum Tunnelling
From what we learned about the Uncertainty Principle, it is not possible for an individual to know the exact speed, location and energy of a particle. It is only possible to have average values (like the "cloud of probability" for position).
Considering this, particles that are considered unable to cross given energy boundaries (based on their amount of energy) are able to pass these boundaries because their given energy is unknown.
Quantum Tunnelling: Continued
The figure on page 622 shows two separate graphs. The first graph is for classical physics and the second graph is for quantum mechanics. As you can see, for the first graph, in order for the electron to be able to get out of the barrier is if the barrier was reduced or if the electron's kinetic energy was increased. On the other hand, the quantum mechanics graph demonstrates the
of the electron's position. With the application of the uncertainty principle to the electron, the particle can be permitted to pass through the barriers if the barrier was narrow enough.
Opaque objects with temperature > 0 radiates photons.
Recall: Black Body Radiation
1884- Johann Balmer invented the relationship that predicted energy levels of sets of spectra lines.
To properly understand what’s happening to an individual atom .
Examining a spectrum emitted by rarefied gas
Spectrums weren't continuous and instead consisted of distinct grouped lines.
We feel the rated photons without touching them:
(Ex. Sunlight) The spectrum is continuous.
Introduced a new model of the hydrogen atom.
Electrons emits energy when drop from a higher energy level to a lower energy level.
Electrons maintain distance from the nucleus because of laws of conservation of energy and angular momentum.
The Bohr Atom
Conservation of Energy:
Assuming angular momentum can be quantified
N is a positive integer that represents the energy level of the electron
Values of h, m k and e are constant, thus simplify and solve for RN
R = RADIUS OF ORBIT
N = QUANTUM #
Conservation of Angular Momentum:
In the year 1927, the uncertainty principle was first proposed by the German physicist named Werner Heisenberg. Heisenberg's main goal was to try to determine the exact location of an electron that was orbiting in an atom.
From his calculations, he later realized that it was impossible for a particle to have a precise position and velocity at the same time. (Partially because subatomic particles exist as waves and as particles. This means that they have wave length and momentum.)
Figure on Page 622.
Why don't large objects tunnel?
It is possible for large objects to tunnel but the probability for them is too much of a small number that it is considered impossible. What may be happening in the larger object is that while one particle has a probability function that allows the object to pass through the barriers, all the other particles don't have the same function.
Sorry about the inconvenience!