Importance of photoelectric effect: Classical physics predicts that any frequency of light can eject electrons as long as the intensity is high enough. Experimental data shows there is a minimum (cutoff frequency) that the light must have. Classical physics predicts that the kinetic energy of the ejected electrons should increase with the intensity of the light. Again, experimental data shows this is not the case; increasing the intensity of the light only increases the number of electrons emitted, not their kinetic energy. THUS the photoelectric effect is strong evidence for the photon model of light.

Wave-Particle Duality The results of the photoelectric effect allowed us to look at light completely different. First we have Thomas Young’s Diffraction experiment proving that light behaved as a WAVE due to constructive and destructive interference. Then we have Max Planck who allowed Einstein to build his photoelectric effect idea around the concept that light is composed of PARTICLES called quanta.

The momentum of the photon Combining E=mc2 and p=mv, you get: p / E = v / c2 The photon travels at the speed of light, so v = c and p / E = 1 / c Therefore the momentum, p, of the photon is p = E / c But we also know that E = hf and λ=c/f, so

This led to new questions…. If light is a WAVE and is ALSO a particle, does that mean ALL MATTER behave as waves? That was the question that Louis de Broglie pondered. He used Einstein's famous equation to answer this question.

YOU are a matter WAVE! Basically all matter could be said to have a momentum as it moves. The momentum however is inversely proportional to the wavelength. So since your momentum would be large normally, your wavelength would be too small to measure for any practical purposes. An electron, however, due to it’s mass, would have a very small momentum relative to a person and thus a large enough wavelength to measure thus producing measurable results. This led us to start using the Electron Microscopes rather than traditional Light microscopes.

The electron microscope After the specimen is prepped. It is blasted by a beam of electrons. As the incident electrons strike the surface, electrons are released from the surface of the specimen. The deBroglie wavelength of these released electrons vary in wavelength which can then be converted to a signal by which a 3D picture can then be created based on the signals captured by the detector.

Line Spectra for a solid object the radiation emitted has a continuous range of wavelengths, some of which are in the visible region of the spectrum. the continuous range of wavelengths is characteristic of the entire collection of atoms that make up the solid. in contrast, individual atoms, free of the strong interactions that are present in a solid, emit only certain specific wavelengths, rather than a continuous range. these wavelengths are characteristic of the atom. a low-pressure gas in a sealed tube can be made to emit EM waves by applying a sufficiently large potential difference between two electrodes located within the tube with a grating spectroscope the individual wavelengths emitted by the gas can be separated and identified as a series of bright fringes or lines. these series of lines are called the LINE SPECTRA.

Bohr Model of Hydrogen atom Bohr tried to derive the formula that describes the line spectra that was developed by Balmer using trial and error. he used Rutherford’s model of the atom, the quantum ideas of Planck and Einstein, and the traditional description of a particle in uniform circular motion. assumptions of Bohr model: electron in H moves in circular motion only orbits where the angular momentum of the electron is equal to an integer times Planck’s constant divided by 2π are allowed electrons in allowed orbits do not radiate EM waves. Thus the orbits are stable. (if it emitted radiation, it would lose energy and spiral into the nucleus) EM radiation is given off or absorbed only when an electron changes from one allowed orbit to another. ΔE = hf (ΔE is energy difference between orbits and f is frequency of radiation emitted or absorbed) Bohr theorized that a photon is emitted only when the electron changes orbits from a larger one with a higher energy to a smaller one with a lower energy.

Life and Atoms Every time you breathe you are taking in atoms. Oxygen atoms to be exact. These atoms react with the blood and are carried to every cell in your body for various reactions you need to survive. Likewise, every time you breathe out carbon dioxide atoms are released. The cycle here is interesting. TAKING SOMETHING IN. ALLOWING SOMETHING OUT!

The Atom As you probably already know an atom is the building block of all matter. It has a nucleus with protons and neutrons and an electron cloud outside of the nucleus where electrons are orbiting and MOVING. Depending on the ELEMENT, the amount of electrons differs as well as the amounts of orbits surrounding the atom.

When the atom gets excited or NOT To help visualize the atom think of it like a ladder. The bottom of the ladder is called GROUND STATE where all electrons would normally exist. If energy is ABSORBED it moves to a new rung on the ladder or ENERGY LEVEL called an EXCITED STATE. This state is AWAY from the nucleus. As energy is RELEASED the electron remove energy by moving to a new energy level or rung down the ladder.

Energy Levels Yet something interesting happens as the electron travels from energy level to energy level. If an electron is EXCITED, that means energy is ABSORBED and therefore a PHOTON is absorbed. If an electron is DE-EXCITED, that means energy is RELEASED and therefore a photon is released. We call these leaps from energy level to energy level QUANTUM LEAPS. Since a PHOTON is emitted that means that it MUST have a certain wavelength.

Energy of the Photon We can calculate the ENERGY of the released or absorbed photon provided we know the initial and final state of the electron that jumps energy levels.

Energy Level Diagrams To represent these transitions we can construct an ENERGY LEVEL DIAGRAM Note: It is very important to understanding that these transitions DO NOT have to occur as a single jump! It might make TWO JUMPS to get back to ground state. If that is the case, TWO photons will be emitted, each with a different wavelength and energy.

Example An electron releases energy as it moves back to its ground state position. As a result, photons are emitted. Calculate the POSSIBLE wavelengths of the emitted photons. Notice that they give us the energy of each energy level. This will allow us to calculate the CHANGE in ENERGY that goes to the emitted photon. This particular sample will release three different wavelengths, with TWO being the visible range ( RED, VIOLET) and ONE being OUTSIDE the visible range (INFRARED)

Energy levels Application: Spectroscopy Spectroscopy is an optical technique by which we can IDENTIFY a material based on its emission spectrum. It is heavily used in Astronomy and Remote Sensing. There are too many subcategories to mention here but the one you are probably the most familiar with are flame tests. When an electron gets excited inside a SPECIFIC ELEMENT, the electron releases a photon. This photon’s wavelength corresponds to the energy level jump and can be used to indentify the element.

Different Elements = Different Emission Lines

Emission Line Spectra So basically you could look at light from any element of which the electrons emit photons. If you look at the light with a diffraction grating the lines will appear as sharp spectral lines occurring at specific energies and specific wavelengths. This phenomenon allows us to analyze the atmosphere of planets or galaxies simply by looking at the light being emitted from them.

Line Spectra of Hydrogen Atom Lyman series occurs when electrons make transition s from higher energy levels with ni = 2, 3, 4, … to the first energy level where nf = 1. notice when an electron transitions from n=2 to n=1, the longest wavelength photon in the Lyman series is emitted, since the energy change is the smallest possible. when the electron transitions from highest to lowest, the shortest wavelength is emitted.