Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
PHYS274 Spring 2017 Homework #6 due this Friday, March 3 – Starting with Photons – Chap 39 in its entirety 1 iClickers reconcile If your iClicker S/N is on this list, See me or send me e-mail so that I can sync #8322EF4E #98741FF3 #A0154EFB #A0F4287C #A112A516 #A4339D0A #A56DE52D #A5724D9A 8 unclaimed (many dropped) Student with no iClicker credit Student ID Registered iClicker #(s) 22875561 019747D1 3x students still haven’t picked up Midterm #1 REMINDER: Set Frequency to A B (default is A A) 2 Q19.1 In the Rutherford scattering experiment, Ernest Rutherford’s students shot what kind of particles at the gold foil target? A. B. C. D. Electrons Protons Neutrons Alpha particles 3 Q19.1 In the Rutherford scattering experiment, Ernest Rutherford’s students shot what kind of particles at the gold foil target? A. B. C. D. Electrons Protons Neutrons Alpha particles Helium nuclei from a radioactive source 4 Q19.2 If you increase the kinetic energy of the electrons in an electron microscope, you will A. B. C. D. Improve the resolution of the microscope Degrade the resolution of the microscope The resolution will remain unchanged. The electrons cannot be captured by the magnetic focus. 5 Q19.2 If you increase the kinetic energy of the electrons in an electron microscope, you will A. B. C. D. Improve the resolution of the microscope Degrade the resolution of the microscope The resolution will remain unchanged. The electrons cannot be captured by the magnetic focus. Why? 6 Q19.3 If you want to reduce the wavelength of the electron by a factor of two in an electron microscope, you A. Decrease the accelerating voltage by half B. Increase the accelerating voltage by 2 times C. Increase the accelerating voltage by 4 times 7 Q19.3 If you want to reduce the wavelength of the electron by a factor of two in an electron microscope, you A. Decrease the accelerating voltage by half B. Increase the accelerating voltage by 2 times C. Increase the accelerating voltage by 4 times V_ba = h^2/(2m e lambda^2) lambda^2 = h^2/(2 m e V_ba) Lambda ~ 1/(sqrt[ V_ba]) 8 “Ultra-violet catastrophy!” Why doesn’t this happen ? Cliffhanger… 9 Review: Breakdown of classical physics (Crisis) • Rutherford’s experiment suggested that electrons orbit around the nucleus like a miniature solar system. • However, classical physics predicts that an orbiting electron (accelerating charge) would emit electromagnetic radiation and fall into the nucleus. So classical physics could not explain why atoms are stable. Question: What is the solution to this crisis ? There is a ground state energy level OK, what does THAT mean? 10 Quantization of atomic energy levels (Experimental) Three classes of spectral features: 11 Quantization of atomic energy levels (visual evidence) 12 Quantization of atomic energy levels • Niels Bohr explained atomic line spectra and the stability of atoms by postulating that atoms can only be in certain discrete energy levels. When an atom makes a transition from one energy level to a lower level, it emits a photon whose energy equals that lost by the atom. • An atom can also absorb a photon, provided the photon energy equals the difference between two energy levels. Insert Figure 39.16 13 Quantization of atomic energy levels • An atom can also absorb a photon, provided the photon energy equals the difference between two energy levels. The master equation for the photon energy in these transitions is 14 Next exercise Are you ready for Bohr Model Bootcamp ? 15 The Bohr model of hydrogen (original argument) • Bohr explained the line spectrum of hydrogen with a model in which the single hydrogen electron can only be in certain definite orbits. Ln=rp=m vn rn • In the nth allowed orbit, the electron has orbital angular momentum nh/2π (see Figure on the right). • Bohr proposed that angular momentum is quantized (this will turn out to be correct in general in quantum mechanics but is not right for the hydrogen atom). 16 The Bohr model of hydrogen Let’s use a different argument based on deBroglie waves to obtain the same conclusions. Think of a standing wave with wavelength λ that extends around the circle. Q: How is the momentum of the atomic electron related to its wavelength ? (remember the Prince) Same as the Bohr quantization condition 17 The Bohr model of hydrogen Now let’s use a Newtonian argument for a planetary model of the atom but use the Bohr quantization condition. (A little hokey). (The mass m is that of the electron.) Balance electrostatic and centripetal forces Here we used the Bohr quantization condition 18 The Bohr model of hydrogen (Bohr radius) Here n is the “principal quantum number” and a0 is the “Bohr radius”, which is the minimum radius of an electron orbital. 19 The Bohr model of hydrogen (iClicker Interlude) A muon is a “heavy electron” (~100 MeV/c^2 vs. 0.5 MeV/c^2) and we are continually bombarded by them They rain down continuously (will cover later), and some of them lose energy and slow down near an atom. Will its orbit? A. Further away B. Nearer to nucleus C. Accelerate inward, destroy the nucleus and all life as we know it ! 20 The Bohr model of hydrogen (Energy levels, derivation) Note that E and U are negative (1/8-1/4=-1/8) This expression for the allowed energies can be rewritten and used to predict atomic spectral lines ! 21 The Bohr model of hydrogen (iClicker check) The velocity of the electron in the ground state, compared with the first excited state (n=2) is A. B. C. D. E. ¼ as fast ½ as fast The same Twice as fast 4 times as fast 1 vn = v1 n 22 The Bohr model of hydrogen (Energy levels) Here R is the “Rydberg constant”, R=1.097 x 107 m-1 Also hcR = 13.60 eV is a useful result. Question: How can we find the energies of photon transitions between atomic levels ? 23 The Bohr model of hydrogen (It works) Here R is the Rydberg constant, R=1.097 x 107 m-1 If nupper=3, nlower=2, let’s calculate the wavelength. Balmer Hα line, agrees with experiment within 0.1% 24 Hydrogen spectrum (also has other spectral lines) • The line spectrum at the bottom of the previous slide is not the entire spectrum of hydrogen; it is just the visible-light portion. • Hydrogen also has series of spectral lines in the infrared and the ultraviolet. 25 Hydrogen-like atoms • The Bohr model can be applied to any atom with a single electron. This includes hydrogen (H) and singly-ionized helium (He+). See the Figure below. Question: How should this formula be modified for singly-ionized helium ? Ans: He has 2p. If an atom is singly ionized, then rnrn/ZEnZ2E But the Bohr model does not work for other atoms; need QM 26 For next time • Photons as Quantum Mechanics gateway Read material in advance Concepts require wrestling with material • Homework #6 available – Due date this Friday, Mar. 3rd 27