Announcements. Reading next class 5.7 Homework 6 due Wednesday. Exam 2 next week (Thursday) Inclusive there will be some SR.

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1 Announcements Reading next class 5.7 Homework 6 due Wednesday. Exam 2 next week (Thursday) Inclusive there will be some SR. Modern physics Photons and PE Atomic spectra Bohr atom etc.

2 Atoms/ Balmer/ Bohr atom

3 A neon lamp emits a red line. Sodium emits a yellow line. What accounts for this difference? a.the electrons in the discharge lamp hit the neon atoms with higher kinetic energy than the electrons hit the sodium atoms b.the electrons in the discharge lamp hit the neon atoms with less speed than the electrons hit the sodium atoms c.the energy spacing between the electronic energy levels that are responsible for these lines are smaller in the neon atom than in the sodium atom. d.the energy spacing between the electronic energy levels that are responsible for these lines is larger in the neon atom than in the sodium atom.

4 What we know so far about atoms: Rutherford: Atoms have a tiny, but very dense core surrounded by a cloud of electrons. p n n n p p n n p n n p Discharge lamps: Atoms struck by fast electrons emit light of distinct colors. 120V Energy levels: Electrons in atoms are found only in discrete energy levels. When they jump down to a lower level, a photon is emitted carrying away the energy. ΔE e ΔE=hf Different Atoms: Different types of atoms have different level structures (seen by the distinct set of colors they emit): Neon: Strong red line; Sodium: strong yellow line

5 increasing energy What do the vertical arrows represent? allowed energies in an atom ground state a. arrows on right represent absorption of light, arrows on left represent emission. b. arrows on both left and right represent emission c. arrows on both left and right represent absorption d. arrows on left represent absorption of light, arrows on right represent emission. e. I don t know. I have never seen such a diagram.

6 increasing energy allowed energies ground state d. arrows on left represent absorption of light, arrows on right represent emission.

7 Energy level diagrams represent energy levels the electron can go to. Different height = different energy Energy e e e e e e For Hydrogen, transitions to ground state in deep ultraviolet! No light emitted with colors in this region because no energy levels spaced with this energy.

8 An single electron bashes into an atom in a discharge lamp Electron leaves hot filament with nearly zero initial kinetic energy 10 V -10eV If atom fixed at the center of the tube, list all the possible photon energies (colors) that you might see? A. 1eV, 2eV, 3eV, 4eV, 7eV, 8eV B. 4eV, 7eV, 8eV C. 1eV, 3eV, 4eV D. 4eV E. Impossible to tell ev -3 ev -6 ev

9 An single electron bashes into an atom in a discharge lamp d - 10 V + D -2 ev -3 ev -6 ev If atom fixed at this point in tube, -10eV list all the possible photon energies (colors) that you might see? A. 1eV, 2eV, 3eV, 4eV, 7eV, 8eV B. 4eV, 7eV, 8eV C. 1eV, 3eV, 4eV D. 4eV Answer is D. Electron only gains about 5eV! E. Impossible to tell. Electron energy = q V = e(ed), where E is the electric field = (battery V)/(total distance D), and d is the distance it goes before a collision.

10 When an emission line appears very bright that means: a.multiple photons are emitted for each single electron transition b.more electron transitions are occurring each second c.the electronic energy levels are farther apart and thus the line appears brighter d.a and b e.b and c Why do I have a problem with this question?

11 When an emission line appears very bright (to an intelligent observer) that means: a.multiple photons are emitted for each single electron transition b.more electron transitions are occurring each second c.the electronic energy levels are farther apart and thus the line appears brighter d.a and b e.b and c Answer is b. Each electron transition produces exactly one photon with energy equal to energy difference between electron energy levels. More electron transitions, more photons, brighter line. But this assumes we ve corrected for what apparent brightness is.

12 Applications of atomic spectroscopy 1. Detecting what kind of atoms are in a material. (excite by putting in discharge lamp or heating in flame to see spectral lines) 2. Detecting what the sun and the stars are made of: Look at the light from a star through a diffraction grating. See what lines there are; Match up to atoms on earth. telescope diffraction star grating 3. Making much more efficient lights! Incandescent light bulbs waste >90% of the electrical energy that goes into them! (<10% efficient) Streetlight discharge lamps (Na or Hg) ~80% efficient. Fluorescent lights ~ 40-60% efficent.

13 Atomic spectra in astronomy L L Let s investigate the internal working of a galaxy R R longer wavelength lower frequency Spectral lines from atoms in stars

14 Hubble and the big bang Spectral lines from Hydrogen Edwin Hubble, PNAS March 15, 1929 vol. 15 no

15 Application: Designing a better light What is important? (Well, we have to be able to see the light!) What color(s) do you want? (red, green & blue is what our eyes can see) How do you excite the atoms to desired level? ( Electron collisions) How to get electrons with desired energy when hit atoms? What determines energy of electrons?

16 Incandescent light (hot filament) Temperature = K Hot electrons jump between many very closely spaced levels (solid metal). Produce all colors. Mostly infrared at temp of normal filament. >90% is worthless Infrared radiation (IR = longer than ~700nm) Discharge lamp Energy levels in isolated atom: Only certain wavelengths emitted. HV P λ IR ~10% of energy is useful visible light Right atom, right pressure and voltage, mostly visible light. Streetlight discharge lamps (Na or Hg) 80% efficient.

17 Florescent Lights. Discharge lamp, but want to have it look white. White = red + green +blue 40-60% efficient (electrical power visible light) How to do this? Converting UV light into visible photons with phosphor. Phosphor converts 180 nm UV to red+ green+blue. 180nm 6.9 ev energy per photon 633nm (red) 2 ev / photon 532nm (green) 2.3 ev / photon 475nm (blue) 2.6 ev / photon } 6.9 ev phosphor wastes 20-30% energy heat

18 Florescent Lights. Discharge lamp, White= Red + green +blue 40-60% efficient (electrical power visible light) Converting 180nm UV light into visible photons with phosphor. phosphor coating Hg 180 nm far UV e Hg Hg Hg Hg discharge lamp/flor. tube 120 V real phosphors more than just 3 phosphor wastes 20-30% energy heat energy of electron in phosphor molecule

19 Energy Summary of important Ideas 1) Electrons in atoms are found at specific energy levels 2) Different set of energy levels for different atoms 3) one photon emitted per electron jump down between energy levels. Photon color determined by energy difference. 4) If electron not bound to an atom: Can have any energy. (For instance free electrons in the PE effect.) Hydrogen Lithium Electron energy levels in 2 different atoms: Levels have different spacing (explains unique colors for each type of atom. (not to scale) Atoms with more than one electron lower levels filled.

20 Now we know about the energy levels in atoms. But how can we calculate/predict them? Need a model Step 1: Make precise, quantitative observations! Step 2: Be creative & come up with a model. Step 3: Put your model to the test.

21 Balmer series: A closer look at the spectrum of hydrogen nm Balmer (1885) noticed wavelengths followed a progression 91.19nm n where n = 3,4,5, 6,. As n gets larger, what happens to wavelengths of emitted light? λ gets smaller and smaller, but it approaches a limit.

22 Balmer series: A closer look at the spectrum of hydrogen nm Balmer (1885) noticed wavelengths followed a progression So this gets smaller Balmer correctly predicted yet undiscovered spectral lines. limit 91.19nm n λ gets smaller and smaller, but it approaches a limit where n = 3,4,5,6,. gets smaller as n increase gets larger as n increase, but no larger than 1/4 4*91.19nm 364.7nm

23 Hydrogen atom Rydberg formula Does generalizing Balmer s formula work? Yes! It correctly predicts additional lines in HYDROGEN. Rydberg s general formula 91.19nm m 2 n Predicts of n m transition: Hydrogen energy levels n (n>m) m (m=1,2,3..) m=1, n=2

24 Hydrogen atom Lyman Series Rydberg s formula 91.19nm m n Hydrogen energy levels 0eV Predicts of n m transition: n (n>m) Can Rydberg s formula tell us what ground state energy is? m (m=1,2,3..) m=1 -?? ev

25 Balmer-Rydberg formula 91.19nm m n Hydrogen energy levels 0eV Look at energy for a transition between n=infinity and m=1 E 0eV initial hc hc 1 1 E final nm m n 0 -?? ev hc nm m E final E 13.6eV 2 m 2 1 m

26 Balmer/Rydberg had a mathematical formula to describe hydrogen spectrum, but no mechanism for why it worked! Why does it work? Hydrogen energy levels Balmer s formula nm nm m n where m=1,2,3 and where n = m+1, m+2 m=1, n=2

27 The Balmer/Rydberg formula is a mathematical representation of an empirical observation. It doesn t explain anything, really. How can we calculate the energy levels in the hydrogen atom? A semi-classical explanation of the atomic spectra (Bohr model)

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