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Lecture Comments (4)

1 answer

Last reply by: Professor Dan Fullerton
Thu May 26, 2016 7:33 AM

Post by Niranjana shankar on May 25 at 08:00:25 PM

Hello Professor,
At 1:53, you said that because electrons are accelerating due to their circular motion, classical physics dictates that photons should be released from the electrons. However, the Centripetal force does not do any work an a rotating object. So, where did the energy to release photons come from? and what part of classical physics dictates that?

1 answer

Last reply by: Professor Dan Fullerton
Wed Apr 16, 2014 7:17 PM

Post by John Parker on April 16, 2014

I'm confused about example 3. To make my confusion clearer, I'll pick one of the arrows that you draw in your explanation, the arrow from n=5 to n=4. Since the electron has to end up at n=2 according to the problem, are you showing that the electron could drop to 4 briefly and, for lack of a better term, "hang out" at 4 before dropping all the way to 2? And you totally lost me when you showed a path from 4 to 2; I thought the electron had to start in 5? Thanks in advance for your help!

Atomic Energy Levels

  • Rutherford showed that atoms has a small, massive nucleus, electrons orbit the nucleus, and most of the atom is empty space.
  • Bohr Model states that electron energy is quantized, they can only exist at specific energy levels, and you can only have a limited number of electrons at each level.
  • When electrons change levels they absorb or emit photons of energy equal to the change in the electron's energy level.
  • X-ray production occurs when electrons knock an electron off a Pt or Mo atom, and an electron from a higher energy level falls into the vacant n=1 state, emitting a high-energy photon.

Atomic Energy Levels

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  1. Intro
    • Objectives
      • Rutherford's Gold Foil Experiment
      • Problems with Rutherford's Model
      • Bohr Model of the Atom
      • Energy Level Diagrams
      • Electron Cloud Model (Probability Model)
      • Atomic Spectra
      • X-Rays
      • Example 1: Electron in Hydrogen Atom
        • Example 2: EM Emission in Hydrogen
          • Example 3: Photon Frequencies
            • Example 4: Bright-Line Spectrum
              • Example 5: Gas Analysis
                • Intro 0:00
                • Objectives 0:09
                • Rutherford's Gold Foil Experiment 0:35
                  • Most of the Particles Go Through Undeflected
                  • Some Alpha Particles Are Deflected Large Amounts
                  • Atoms Have a Small, Massive, Positive Nucleus
                  • Electrons Orbit the Nucleus
                  • Most of the Atom is Empty Space
                • Problems with Rutherford's Model 1:31
                  • Charges Moving in a Circle Accelerate, Therefore Classical Physics Predicts They Should Release Photons
                  • Lose Energy When They Release Photons
                  • Orbits Should Decay and They Should Be Unstable
                • Bohr Model of the Atom 2:09
                  • Electrons Don't Lose Energy as They Accelerate
                  • Each Atom Allows Only a Limited Number of Specific Orbits at Each Energy Level
                  • Electrons Must Absorb or Emit a Photon of Energy to Change Energy Levels
                • Energy Level Diagrams 3:29
                  • n=1 is the Lowest Energy State
                  • Negative Energy Levels Indicate Electron is Bound to Nucleus of the Atom
                  • When Electron Reaches 0 eV It Is No Longer Bound
                • Electron Cloud Model (Probability Model) 4:46
                  • Electron Only Has A Probability of Being Located in Certain Regions Surrounding the Nucleus
                  • Electron Orbitals Are Probability Regions
                • Atomic Spectra 5:16
                  • Atoms Can Only Emit Certain Frequencies of Photons
                  • Electrons Can Only Absorb Photons With Energy Equal to the Difference in Energy Levels
                  • This Leads to Unique Atomic Spectra of Emitted and Absorbed Radiation for Each Element
                  • Incandescence Emits a Continuous Energy
                  • If All Colors of Light Are Incident Upon a Cold Gas, The Gas Only Absorbs Frequencies Corresponding to Photon Energies Equal to the Difference Between the Gas's Atomic Energy Levels
                  • Continuous Spectrum
                  • Absorption Spectrum
                  • Emission Spectrum
                • X-Rays 7:36
                  • The Photoelectric Effect in Reverse
                  • Electrons Are Accelerated Through a Large Potential Difference and Collide with a Molybdenum or Platinum Plate
                • Example 1: Electron in Hydrogen Atom 8:24
                • Example 2: EM Emission in Hydrogen 10:05
                • Example 3: Photon Frequencies 11:30
                • Example 4: Bright-Line Spectrum 12:24
                • Example 5: Gas Analysis 13:08

                Transcription: Atomic Energy Levels

                Hi everyone and welcome back to 0000

                I am Dan Fullerton and today we are going to continue our study of modern physics as we talk about atomic energy levels. 0003

                Our goals are going to be to explain the significance of Rutherford's gold foil experiment, identify some shortcomings in his model of the atom and describe the assumption of Bohr's model of the hydrogen atom. 0009

                We will utilize energy level diagrams to determine characteristics of absorbed and emitted photons, we will explain the production of absorption and emission spectra and understand the nature and production of x-rays. 0020

                Let us start by talking about Rutherford's gold foil experiment. 0034

                J.J. Thompson had previously shown that atoms contained small negative particles known as electrons. 0038

                He started to get an idea of charge to mass ratio here, but much beyond that was unknown until in the early 1900s, New Zealand physicist, Ernest Rutherford, shot some alpha particles, which are Helium nuclei, at a very thin sheet of gold foil and then looked at the deflection of those particles. 0045

                If we have an alpha particle source shot at a gold foil and then look to see what would happen and he saw that most of the particles went through and deflected, but some alpha particles were deflected very large amounts. 0065

                He was able to make a couple of key conclusions: atoms have a small, massive positive nucleus; electrons orbit the nucleus, and most of the atom, therefore, must be empty space. 0077

                There were some problems with this model though. 0092

                The electrons do not emit continuous radiation. 0095

                What you would expect if charges are moving in a circle; they are accelerating, therefore classical physics predicts that they should release photons. 0098

                If they release photons, they should be losing energy and if they are losing energy, their orbits should be degrading and eventually they should become unstable. 0105

                The electron should crash in the nucleus, but that does not happen. 0115

                Elements were also found to emit and absorb electromagnetic radiation only at specific frequencies, which did not correlate to Rutherford's theory. 0119

                So, this needed to be refined and along came Danish physicist Niels Bohr. 0128

                He traveled to the UK to join Rutherford and his research group and he ended up winning the Nobel Prize in 1922 for his work. 0132

                He said that electrons do not lose energy as they accelerate, the energy of the electron is quantized; it comes in specific amounts, not a continuous spectrum of amounts. 0140

                And electrons can only exist at specific, discreet energy levels. 0149

                Now each atom was allowed only a limited number of specific orbits or electrons at each energy level and in order to change energy levels, the electrons must absorb or emit a photon corresponding to that exact difference in energy levels. 0154

                If they want to move up to a higher energy level, they have to absorb a photon with exactly that amount of energy. 0168

                If they want to drop down an energy level, they are going to emit a photon with that exact amount of energy. 0175

                He came up with an equation to tell you what that energy was. 0180

                The energy required to go to a specific energy level or of a specific energy level is equal to the square of the atomic number times -13.6 electron-volts over the square of the energy level. 0185

                Now this only worked for small atoms; it does not work for everything, but it was pretty good for small atoms as a starting point. 0201

                Let us take a look at an energy level diagram. 0210

                N = 1 down here is the lowest state and you can think of this almost as the energy well we were talking about previously, where if there is an electron at the ground state it is trapped by hydrogen in here and to get out it must give up, it must find, or absorb a photon of at least 13.6 electron-volts to be free. 0213

                If it absorbed a photon of 14.6 electron-volts, it would have enough to get free and it would have 1 eV left over; that would be its kinetic energy. 0232

                Now the energy levels here are negative and that indicates that the electron is bound to the nucleus of the atom; it cannot leave and it is not free until it pays at least -13.6 eV or it pays 3.4 eV if it is at the N = 2 state, or whatever state it is in. 0242

                When the electron reaches 0 state, ionization, it is no longer bound and it can be emitted as a photoelectron. 0260

                Now while we are here looking at the hydrogen energy level diagram, one of the famous series is called the Balmer series. 0267

                That is a set of visible spectral lines created by electrons falling in hydrogen to the N = 2 level. 0277

                Now there is a little bit more to the story than we have talked about so far, there is a lot more to the story.0286

                But an electron only has a probability of being located in certain regions surrounding the nucleus and electron orbitals are really these probability regions. 0292

                So if we want to get much more specific, we have to start looking at probability and statistics to talk about where electrons are, are not, and what their likelihood is of being in a specific position or not being in a specific region or specific position. 0300

                Let us talk about atomic spectra. 0317

                If atoms can only emit certain frequency of photons corresponding to the difference in energy as the electron falls from a high energy level to a low energy level, you are going to get only certain frequencies emitted. 0319

                That is going to give you specific discreet spectra. 0330

                They can only absorb photons with those energy levels as well, so you get very, very unique spectra for each of these different types of elements. 0334

                How it works -- If an object is hid to the point where it glows or in incandescence, it emits a continuous energy spectrum.0344

                On the other hand, things like gas discharge lamps, they emit light by exciting electrons to higher energy states when the electrons fall back down to their lower energy states, they emit a photon and that photon is emitted at that specific frequency, corresponding to the difference in energy between the energy levels. 0350

                Therefore, you are going to get a unique discreet spectra; you are only going to get photons emitted at specific frequencies at specific colors. 0367

                If all colors of light are incident upon a cold gas, the gas can only absorb the frequencies corresponding to increases in energy level, so all colors of light going into a cold gas...0376

       is only going to absorb the ones that allow electrons to jump to high energy levels and what you are going to get out are all the colors except the ones that are absorbed. 0388

                That is called an absorption spectrum. 0397

                Let us take a look at these. 0400

                If we have something like incandescence white light, we are going to put it through a prism, then we can see that we have all frequencies and all colors of lights. 0401

                On the other hand, if we shine white light through a cold gas and then separate it out, we are going to see that the only colors missing are going to be the ones that correspond to jumps in energy levels for the electrons because that is what is absorbed in the cold gas. 0410

                Or if we create an emissions spectrum, we take a hot gas, we excite the gas, the electrons in the gas, the higher energy levels, and when they fall down they emit photons at those specific frequencies. 0427

                So when we separate that spectrum, what we are going to see is lines of light at specific frequencies, or specific colors. 0440

                These are going to correspond to exactly the holes in the absorption spectrum assuming it is the same element in your gas. 0447

                Now x-ray production is basically the photoelectric effect in reverse. 0457

                X-rays can pass through light materials and we know that; we have done that at the doctor's office when we have broken a bone and they go show you how it is passed through your skin and a part gets absorbed by the bone and they can see what is inside of you. 0462

                Now electrons, the way they are formed, you accelerate electrons through a large potential difference and you have them collide with a plate made of Molybdenum or Platinum. 0472

                When you do that you knock electrons out of the lowest and equals one energy state, then electrons in the atoms of the metal must fall down to feel that in equal's one state. 0482

                As they fall down, they emit a photon and that photon has enough energy that it is an x-ray. 0492

                It has a large amount of energy, so that is the typical way we are going to form x-ray photons. 0497

                Some examples here -- An electron in a hydrogen atom drops from the N = 3 to the N = 2 state. 0505

                Determine the frequency of the emitted radiation. 0514

                Well the energy of the photon that is emitted is going to be its initial energy minus its final energy. 0517

                Its initial was -1.51 eV and its final is going to be -3.4 eV, so the energy of our photon is 1.89 eV. 0526

                Now, we need to convert that to joules, so 1.89 eV times -- well we want electron-volts to go away and we want joules and 1 eV = 1.6 × 10-19 J. 0545

                Electron-volts make a ratio of 1 and I come up with an energy in joules of about 3.02 × 10-19. 0560

                Now that we have that, let us determine the frequency. 0569

                If energy equals Hf, then frequency is energy over (h) or 3.02 × 10-19 J over Planck's constant, 6.63 × 10-34, which implies that the frequency is going to be about 4.56 × 1014 Hz. 0573

                Let us take a look at another one. 0603

                Determine the energy in electron-volts and joules of a photon emitted by an electron as it moves from the N = 6 to the N = 2 state. 0605

                Is this the only energy that an electron in the N = 6 energy level could emit? 0616

                Well, absolutely we know the answer to this part is no. It could go from 6 to 5, 6 to 4, 6 to 3. 0621

                It could go in many other ways to emit other energies of photons. 0626

                Now let us figure out what the energy is of the photon as it goes from 6 to 2. 0630

                Well, our energy of our photon is going to be the initial minus the final energy. 0635

                It starts at -.38 eV minus the final, which is -3.4 eV, therefore, the energy of the photon and electron-volts is just going to be about 3.02 eV. 0642

                To convert that to joules, we will start off with 3.02 eV and we want electron-volts to go away, so we will put that in the denominator. 0660

                We want joules and 1 eV = 1.6 × 10-19, therefore the energy in joules is going to be about 4.83 × 10-19 J. 0669

                Another one -- According to the Bohr model of the hydrogen atom, an electron dropping from the 5th energy level and eventually landing in the 2nd energy level could produce photons of how many different frequencies? 0691

                Let us draw a poor man's energy diagram -- 5th level, 4th level, 3rd level, 2nd level and let us see how many paths we have from 5 down to 2. 0702

                We could go from 5 to 4; there is 1, 2, 3; we could go from 5 to 3 and there is 4. 0715

                We could go from 5 all the way to 2; there is 5 and we could go all the way from 4 to 2, so 6 different photon frequencies could be produced by this transition depending on the path the electron took on its way down to that final state. 0724

                The bright line emission spectrum of an element can best be explained by electrons transitioning between discreet energy levels in the atoms of that element -- well that sounds promising. 0745

                Protons acting as both particles and waves -- not sure what that has to do with our problem. 0756

                Photons scattering electrons demonstrating the Compton Effect -- it had nothing to do with our bright line emission spectrum. 0763

                Protons being dispersed uniformly throughout the atoms of that element -- not really sure even what that means. 0769

                So our best answer must be A, the bright line emission spectrum is caused by electrons transitioning between discreet energy levels in the atoms of that element. 0774

                Let us try one last sample problem. 0785

                The diagram below represents the bright line spectra of 4 elements, A, B, C, and D and the spectrum of an unknown gas sample. 0789

                Based on the spectra, which two elements are found in the unknown sample? 0797

                Well, what I am going to do here is if this is my unknown sample, I need to find where we have lines that match up from these different elements. 0801

                On the unknown sample, I have a line right there and that looks like it could correspond to element (B) and that also would correspond to (B), so I am pretty sure that we have some (B) in our sample. 0809

                Let us see what else we have. 0824

                We have two lines here in (C) and we have those two lines and that also corresponds here and here and that covers all of the lines, so I would say that we must have (B) and (C) in our unknown sample. 0827

                Our unknown sample would be made up of elements of (B) and (C) and this is one way you can do gas analysis to figure what an unknown sample is made out of. 0843

                Hopefully that gets you a good start on atomic energy levels. 0853

                Thanks so much for watching us here at Make it a great day everyone!0856