Quantum Mechanics Lab

Lasers, Section 28-11, p.820 (text). The acronym LASER stands for “light amplification by stimulated emission of radiation” and the first one was invented by Hughes Laboratories in Malibu, Ca, in 1960. In brief, it had a synthetic ruby rod, from which the laser beam would emerge, surrounded by a lamp that pumped or stimulated the ruby “atoms” (aluminum oxide) into emitting red light. The cylindrical ruby rod must have mirrors on its ends, separated by a multiple of the emitted light’s wavelength. The above figure shows the lamp surrounding the ruby rod, and the emergent laser beam. The theory for this now follows. We are starting with Figure 28-18, p. 821, ruby laser, “Creating an Inverted Population”. Here the lamp is greenish-yellow, 564 nm wavelength. Recalling that E = h f, f = c/λ and converting the E to eV, 564 nm is 2.2 eV. The 2.2 eV excites the ruby “atoms” from their ground state E0, to the excited state E2. Near E2 and slightly below it, is a second state for the ruby “atoms” E1, of 1.8 eV. Excited electrons at E2 randomly drop down to E1, and photons emitted here would be in the “far infrared, not useful”. But then E1 electrons drop down again to the ground state Eo, and this 1.8 eV drop emits 694 nm photons, which are red. Should these photons collide with other electrons at E1, they will stimulate an additional 694 nm photon. We need more electrons at E1 than E2, an “inverted population” for this to happen. This occurs if the lifetime of the E1 electrons is longer than the lifetime of the E2 electrons. This is called “inverted” because the E1 level is below E2. So, if the population at E1 is greater than E2, pairs of photons are produced; this “amplification” creates strong red light in the ruby crystal. Mirrors on either end of the crystal “bounce” the amplified red photons “back and forth”, building up further amplification. As shown in the figure, the left mirror is ideally 100% reflective, while the right mirror is less, to “let the red light out” as a focused beam. If the mirrors “are precisely a multiple of the 694 nm wavelength apart”, then the emergent laser beam has all its red photon crests “lining up” as constructive interference, and this beam is said to be “coherent”. The above description allows us to set up and simulate a ruby laser with all these properties. https://phet.colorado.edu/sims/cheerpj/lasers/latest/lasers.html?simulation=lasers Pull up the simulation. Click on the upper right-hand tab “Multiple Atoms (Lasing). On the right, click on Energy Levels 3 and Enable Mirrors. Then on Mirror Reflectivity (%), pull down to 70 % (or close to this). This is for the right hand mirror (the left is always 100 %). Next we have the Lamp Control, the upper tab is intensity so pull it all the way to the right, and below this pull the║so it is in the greenish yellow location as is shown. At this point, the lamp at 564 nm is not exciting the atoms to the too high upper E2 level, “no lasing”. We need to “Configure atoms’ electronic energy levels”, so that the lamp excites the electrons into the upper level (labeled as a blue-circled 3). Pull this upper level down as far as possible—it will sit on top of the red-circled level 3—and you can see the electrons in upper-level 3 “populating” while the atoms in the tube are visibly being excited green and red. The red level 3 also has plenty of electrons populating it. Now we look at “Laser Power” level bars, Internal Power and Output Power. We see occasional red photons exiting the right mirror, sometimes in pairs. When so both Powers may be as much as 1 bar. Our laser has yet to produce a beam. What else might we do, to get a good beam out of the laser? Answer: reduce the upper level’s lifetime, meaning these electrons more immediately jump down to the red-labeled level. Then, more electrons in the red-labeled level gives more red photons, and these impact other red-level electrons, stimulating red photon pairs. This is when “stimulated” amplification occurs, and the laser produces a beam. We reduce the upper level’s lifetime, pulling its Lifetime tab to the left (upper right, as shown in the above figure). Do this and wait as the laser stabilizes. Finally “green” internal power, and several bars of output power (per above figure). 1. Watch the output beam, and estimate the percentage of paired photons vs. overall photons: ____ % (2 sig fig) 2. Move Mirror Reflectivity to 100 %. Is there an output Beam? Yes/No. After 2 minutes, what happens? ____ __ (2 words) 3. Do an exact calculation of E1 in the upper right figure. Use E = h f, f = c / λ, h = 6.63E-34, c = 3E8 m/s and 1 eV = 1.6E-19 J. Thus E1 = _____ eV (3 sig figs, using above values of h, c, and 1 eV) (note the text error, 2.20 eV is 564 nm not 550 nm) Subatomic Particles: protons, neutrons, and electrons The lecture describes atoms as protons, neutrons and electrons. Protons and neutrons in the nucleus, electrons orbiting the nucleus. The atomic number gives the number of protons, and the location of the atom on the Periodic Table. Electrically neutral atoms have their number of electrons (− charged) matching their number of protons (+ charged). The organization of the electrons into shells and subshells, determines an atom’s chemical properties; and thus atoms get organized into columns on the Periodic Table with similar properties in any given column. In the simple labs below, our objective is in describing the nucleus further, in terms of protons and neutrons. We will do this by “building up atoms with protons, neutrons and electrons”, “building isotopes” and “building a nucleus”. Build an atom: pull up https://phet.colorado.edu/sims/html/build-an-atom/latest/build-an-atom_all.html Click on the Atom box, pull a proton into the nucleus ×, and an electron onto the 2nd shell (goes to 1st shell as it should). The Periodic Table shows H for hydrogen upper left, and neutral atom is indicated. Click on the Show Stable/Unstable at the extreme lower-right, and we immediately see that it is neutral Hydrogen with 1 proton and 1 electron and is stable. Pull another proton into the nucleus, unstable and labeled + Ion. Helium. Pull a neutron into the nucleus, now stable. For Helium, pull another electron “up and onto” the 2nd shell (goes across to 1st shell). Neutral Atom. Pull another 4 protons into the nucleus, unstable and labeled + Ion. Carbon. Pull 5 neutrons into the nucleus, now stable. This is known as “Carbon-12”, the 12 being its mass # = #protons + #neutrons. It is the stable form of carbon. The electrons need to be 6 for a neutral atom, so pull 4 more electrons and watch, all go onto the 2nd shell as they should. What about its isotope, Carbon-14? Carbon always has 6 protons, but now would have 8 neutrons for mass # = 14. Pull another 2 neutrons onto the nucleus, and click on Mass Number (below the Periodic Table) to see the 14. 4. Is this isotope stable or unstable? Circle one. Isotope means same atom or #protons, but differing #neutrons. Build an isotope: pull up https://phet.colorado.edu/sims/html/isotopes-and-atomic-mass/latest/isotopes-and-atomic-mass_all.html Click on the Isotopes box. 5a. This comes up with a Hydrogen atom sitting on the scale. Hydrogen-1. Mass# = __. #neutrons = __. Stable or Unstable. b. Pull a gray neutron into its nucleus. This isotope is now Hydrogen-__. Mass# = __. #neutrons = __. Stable or Unstable c. Pull a 2nd neutron into its nucleus. This isotope is now Hydrogen-__. Mass# = __. #neutrons = __. Stable or Unstable d. Click on Carbon “C” on the upper right Periodic Table portion: This isotope is now Carbon-___. Mass# = ___. #neutrons = ___. Stable or Unstable Add 2 neutrons, now Carbon-___. Mass# = ___. #neutrons = ___. Stable or Unstable Build a nucleus: pull up https://phet.colorado.edu/sims/html/build-a-nucleus/latest/build-a-nucleus_all.html Click on Decay box. At the very bottom, notice an orange up arrow to the left of protons, and gray up arrow to the right of neutrons. 6. Click once on the orange up arrow to the left of protons. Electron Cloud is checked on, and it’s a hydrogen atom. Observe from the top to the right, Half-life: ∞ Stable Hydrogen-1 and Available Decays all grayed out Click up arrow, right of Neutrons, Half-life: ∞ Stable Hydrogen-2 and Available Decays all grayed out Click up arrow, right of Neutrons, Half-life: 3.9×108 s Unstable Hydrogen-3 and Available Decays: β- decay Let’s now discuss unstable and decays more fully. A nucleus will decay when its #protons and #neutrons aren’t “roughly” equal. Hydrogen-3 has twice as many neutrons as protons, not “near equal”, so it will “try” to reject its extra neutron. This gives β- decay. The neutron “decays” to a proton + electron, wow, and the net charge is still zero. (neutron always has zero charge to begin with). Fully understanding this involves the “strong and weak nuclear forces, not a topic in PHYS 2B. But it’s still worth “knowing a little”. Another type of decay occurs when there are too many protons not “near equal” to the number of neutrons. Protons are “like charged” and will repel one another, and one gets expelled from the nucleus. 6a. Click up arrow twice, left of Protons, Half-life: _________ s Stable/Unstable Lithium-__ Fill in number circle one name-number and Available Decays: ________________ fill in Too many protons, will decay by ejecting one, very shortly after it forms Click up arrow 4 times, right of Neutrons, Half-life: 1.8×10-1 s Unstable Lithium-9 and Available Decays: β- decay (Beta−) 6b. Click up arrow 3 times, left of Protons, Half-life: ∞ Stable/Unstable Carbon-12 and Available Decays: none circle one 6c. Click up arrow twice, right of Neutrons, Half-life: _______ s Stable/Unstable ______-__ and Available Decays: _____ Fill in number circle one name-number fill in We’ve looked at Carbon-12 and Carbon-14 in all the above simulations. Carbon-12 is stable, and Carbon-14 decays in about 5700 years (a day is 86,400 s and 1 year is 365 days). This fact is used to date carbon-containing objects by archeologists. The decay time is called the “half-life”, so after 5700 years half the Carbon-14 remains, and after 2 half-lives “half of half” or ¼ remains (½ of ½ is ½ x ½ = ¼ = 25%) after 2×5700 = 11,400 years. 6d. How much Carbon-14 would remain after 17,100 years? ____ %. A very precise mass spectrometer (as we’ve studied) is used to isolate the heavier Carbon-14 from Carbon-12 in a sample, to determine the experimental % and thus age in terms of the 5700 years half-life, also called “lifetime”.

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