QUANTUM MECHANICS Birth of Quantum Mechanics WAVE PARTICLE

QUANTUM MECHANICS Birth of Quantum Mechanics

WAVE – PARTICLE DUALITY • Let’s revisit Dr. Quantum • https: //www. youtube. com/watch? v=Df. Pepr. Q 7 o. Gc • So, now that we know this happens, we need to ask ourselves, what lead physicists down the path to recognize that EMR can act as both a wave and a particle.

END OF AN ERA • At the end of the 1800 s, physicists looked back at a period of 300 years of great growth. • Newton had explained the motion of objects here on earth (and in the heavens). • Maxwell had put together electricity and magnetism in his work on electromagnetic radiation. I. E We knew what an Electromagnetic wave looked like. • Thomson had figured out the mass of atomic particles and so much more! • For the most part, Physicist believed they have solved all the problems of the universe – but things were going to get even more complex than they ever imagined.

CLASSICAL PHYSICS • Up to now, what we have been studying is known as classical physics: • • • Kinematics Dynamics Momentum Energy Waves Mechanics • For almost all physical interactions in the universe we are able to solve using classical physics, but classical physics was unable to solve a few physical (and chemical) problems: • Blackbody Radiation • Photoelectric

BLACKBODY RADIATION • A blackbody is an object that perfectly absorbs all wavelengths of EMR that strike it. We humans are a blackbody as we absorb all the wavelengths of EMR from any light (Sun lightbulbs, Infrared waves Ultraviolent waves. ) • This means that all EMR, from the lowest frequency to the highest frequency will perfectly be absorbed by the object. • Note it is called a blackbody, since objects colored black absorb all visible light that falls on them. Cavity Radiation AKA Blackbody Radiation

BLACKBODY RADIATION • This energy that is absorbed is also perfectly re-emitted and released by the object as EMR. • According to classical physics, as the frequency of the emitted EMR increases, so should the intensity (the vibration of the atoms in the object). • As more and more energy from the EMR was absorbed, it would cause the atoms of the blackbody to vibrate faster and faster at higher and higher frequencies. • These vibrating atoms (made of charged particles) would release higher and higher frequencies of more and more intense EMR. • This classical physics explanation of the emitted EMR could be drawn as a graph.

BLACKBODY RADIATION • Buuuuuuuttttt……. The problem is, this doesn't happen! • Instead, the intensity of the emitted radiation does increase, until it reaches a particular frequency of intensity which is also dependent on the temperature of the object. • STOP AND THINK – imagine a lightbulb giving off EMR. The glass bulb itself is a cavity as it is being hit constantly by EMR. Classical Physics suggests that if the bulb was being bombarded by light waves and the electrons in the bulb were vibrating faster and faster, then the intensity of the radiation leaving the bulb would never peak and eventually the glass would explode. BUT IT DOES NOT. Bizarre…. • PHET Simulation of blackbody radiation.

BLACKBODY RADIATION • As observed in experiments the following graph indicates that after a specific amount of EMR frequency hitting the object, the intensity of the EMR being released will hit a point where curves back down.

BLACKBODY RADIATION • These graph’s contrast to what classical physics (wave theory) suggested should happen. Classical Physics vs Quantum Mechanics

SOLVING THE BLACKBODY RADIATION • Late in the year 1900, Max Planck (pronounced “Plonk, ”) came up with a new idea that would solve the problems everyone was having when trying to explain blackbody radiation. • Up to this point everyone was assuming that those little vibrating electrons (thought to be absorbing and then re-emitting the blackbody radiation) could vibrate at any frequency. • Planck suggested that atoms emit radiation only at a particular moment when their vibrational energy changes. Thus, there is a minimum amount of energy that a particular frequency of EMR can transfer.

ENERGY OF VIBRATION • E = nhf • WHERE E = Energy in Joules n = number of photons, nth state of vibration energy level of orbits in an atom. h = Planks constant – 6. 626 x 10 -34 J/Hz (or J/s). OR 4. 14 x 10 15 -e. V· s where 1 e. V = 1. 602677· 10 -19 J f = is the frequency of vibration of the atom in Hertz (Hz)

Using the PHET simulation hydrogen we can examine how this idea works. Electron Excitation Light Emission + n=1 n=2 n=3

ENERGY LEVELS • Ephoton = |Ef – Ei| • If Ef > Ei than a photon is absorbed. If Ef < Ei than a photon is emitted (we can see this as light).

PLANKS EQUATION • Planks Equation really solves how much energy a photon (or the wave) has and it can be rewritten as follows: E = hf WHERE E = Energy in Joules h = Planks constant – 6. 626 x 10 -34 J/Hz (or J/s). OR 4. 14 x 10 15 -e. V· s where 1 e. V = 1. 602677· 10 -19 J f = is the frequency of vibration of the atom in Hertz (Hz)

EXAMPLE # 1 • Determine the smallest amount of energy from a light source that emits light at a frequency of 4. 50 e 14 Hz. E = hf E = 6. 63 e-34 (4. 50 e 14) E = 2. 9835 e-19 = 2. 98 e-19 J

EXAMPLE #2 •

ALBERT EINSTEIN • In 1905 an unknown physicist named Albert Einstein came up with an idea that built on Planck’s theory. • Planck thought that his ideas of quanta and E = hf was all about how matter absorbed and emitted energy. • Remember, he was focused on explaining blackbody radiation. • Einstein suggested that these ideas were primarily about the light itself. • He figured that light itself was where it all started, that the light itself was made up of individual pieces. • The reason this was so radical an idea was because it meant that light was acting like a particle. • The light particles were eventually named photons.

EXAMPLE #3 • You buy a laser at the store and read on the label that it has a frequency of 4. 38 x 1015 Hz. The label also says that it runs at 4. 06 m. W. Determine how many photons it can release in one second. • First, determine how much energy the laser can put out in one second, then use Planck’s equation E=nhf and solve for ’n’ the number of photons. P=ΔE/t Δ E=Pt Δ E=4. 06 x 10 3 -J E=nhf n= E/hf n= 4. 06 x 10 3 -J/ 6. 63 x 104. 38)34 - x 10 (15 n=1. 3981005 x 1015 photons 1. 40 x 10 15 photons