Bohr s atomic model
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Bohr s atomic model

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Chapter 2, Atomic Physics. 2. Nankai University, CY Li 2012/6/30. Some words. BlackbodyAbsorb, emitSpectrumUltraviolet catastropheIncident photoelectric effectFrequencyCompton effect. Discrete spectraRydberg constantorbital angular momentaquantum numberquantum mecha
Bohr s atomic model

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1. Chapter 2, Atomic Physics 1 Nankai University, CY Li 2012/6/30 Bohr?s atomic model Four puzzles Blackbody radiation The photoelectric effect Compton effect Atomic spectra Balmer formula Bohr?s model Frank-Hertz experiment

2. Chapter 2, Atomic Physics 2 Nankai University, CY Li 2012/6/30 Some words Blackbody Absorb, emit Spectrum Ultraviolet catastrophe Incident photoelectric effect Frequency Compton effect Discrete spectra Rydberg constant orbital angular momenta quantum number quantum mechanics

3. Chapter 2, Atomic Physics 3 Nankai University, CY Li 2012/6/30 Blackbody Thermal radiation: electromagnetic radiation emitted by hot objects, at room temperature? Absorptivity (absorptance): the ratio of the radiation absorbed by a body to that incident on the body. Blackbody: A body with a surface having an absorptivity equal to unity. A realistic blackbody: For a cavity kept at a constant temperature with the interior wall blackened, a small hole in the wall behaves like a blackbody. At room temperature the thermal radiation is mostly in the infra-red region. Absorptance: absorptive power Thermal radiation: If a body is in thermal equilibrium with its surroundings, it must emit and absorb the same amount of energy per unit time.At room temperature the thermal radiation is mostly in the infra-red region. Absorptance: absorptive power Thermal radiation: If a body is in thermal equilibrium with its surroundings, it must emit and absorb the same amount of energy per unit time.

4. Chapter 2, Atomic Physics 4 Nankai University, CY Li 2012/6/30 Some observations Stefan's Law states that the power radiated by a body is proportional to the 4th power of the absolute temperature. For a given temperature, the radiation forms a continuous spectrum with respect to the frequency. The total power emitted per unit area (total emittance) is proportional to the fourth power of the absolute temperature, Stefan?s law: The total power emitted per unit area (total emittance) is proportional to the fourth power of the absolute temperature, Stefan?s law:

5. Chapter 2, Atomic Physics 5 Nankai University, CY Li 2012/6/30 Wein's Displacement Law The shift is the frequency at which radiant power is maximum is very important for trapping solar energy, such as in green house. We need glass to allow the solar radiation in, but not let it out. This is due to the two radiations are in very different frequency ranges (5700K and 300K). The radiation from the human body is in the infrared portion of light.The shift is the frequency at which radiant power is maximum is very important for trapping solar energy, such as in green house. We need glass to allow the solar radiation in, but not let it out. This is due to the two radiations are in very different frequency ranges (5700K and 300K). The radiation from the human body is in the infrared portion of light.

6. Chapter 2, Atomic Physics 6 Nankai University, CY Li 2012/6/30 Reyleigh-Jeans law The amount of radiation emitted in a given frequency range is proportional to the number of resonant modes (standing waves). They showed that the number if proportional to the frequency squared. The amount of radiation emitted in a given frequency range is proportional to the number of resonant modes (standing waves). They showed that the number if proportional to the frequency squared.

7. Chapter 2, Atomic Physics 7 Nankai University, CY Li 2012/6/30 Ultraviolet catastrophe

8. Chapter 2, Atomic Physics 8 Nankai University, CY Li 2012/6/30 Puzzles in blackbody radiation Two puzzles: Why were not radiation above the ultraviolet region present? Why was there a non-uniform distribution of electromagnetic radiation being emitted? Two puzzles in other words: 1: Why were not X-rays and gamma rays emitted form the blackbody? 2: Why was the read frequency radiation more predominant than the blue?Two puzzles in other words: 1: Why were not X-rays and gamma rays emitted form the blackbody? 2: Why was the read frequency radiation more predominant than the blue?

9. Chapter 2, Atomic Physics 9 Nankai University, CY Li 2012/6/30 Plank?s theory Planck made an assumption that the energy of an oscillator must be an integral multiple of the product of the constant h and the frequency of the electromagnetic radiation it emitted. His assumption resulted in a formula for the blackbody radiation that was in excellent agreement with experiment at all frequencies. His position was a little like that of a student who has peeked at the answer in the back of the book and is now faced with the task of showing how to logically reach the answer. He claimed that the electromagnetic radiation from the blackbody was emitted by atoms.His position was a little like that of a student who has peeked at the answer in the back of the book and is now faced with the task of showing how to logically reach the answer. He claimed that the electromagnetic radiation from the blackbody was emitted by atoms.

10. Chapter 2, Atomic Physics 10 Nankai University, CY Li 2012/6/30 Two puzzles to be explained Radiation in the high frequency region were not emitted from the blackbodies because this required large energy changes which could not occur in the atoms. Certain energy states were more probable in the atoms and therefore frequencies associated with these energy states were more likely to be emitted.

11. Chapter 2, Atomic Physics 11 Nankai University, CY Li 2012/6/30 The photoelectric effect When light of a high frequency was incident on a metallic surface, electrons were emitted from the surface. The radiation causes the metal to emit electrons. It was first found by Hertz. Bunn, P503The radiation causes the metal to emit electrons. It was first found by Hertz. Bunn, P503

12. Chapter 2, Atomic Physics 12 Nankai University, CY Li 2012/6/30 Actual observation Intensity: The high intensity of light would not cause electrons to have high KE. The actual reaction time is very short (10-9s). Frequency: At a certain frequency called threshold frequency, electrons were emitted. A frequency beyond it will cause the electrons to have a greater KE. Stopping voltage: The energy of the ejected electrons was proportional to the frequency of the illuminating light & had nothing to do with intensity. Three variables: the intensity of light, the frequency of light, the voltage across the plates. The electrons were emitted immediately - no time lag! 2. Increasing the intensity of the light increased the number of photoelectrons, but not their maximum kinetic energy! 3. Red light will not cause the ejection of electrons, no matter what the intensity! 4. A weak violet light will eject only a few electrons, but their maximum kinetic energies are greater than those for intense light of longer wavelengths! the opposing voltage it took to stop all the electrons gave a measure of the maximum kinetic energy of the electrons in electron volts. Three variables: the intensity of light, the frequency of light, the voltage across the plates. The electrons were emitted immediately - no time lag! 2. Increasing the intensity of the light increased the number of photoelectrons, but not their maximum kinetic energy! 3. Red light will not cause the ejection of electrons, no matter what the intensity! 4. A weak violet light will eject only a few electrons, but their maximum kinetic energies are greater than those for intense light of longer wavelengths! the opposing voltage it took to stop all the electrons gave a measure of the maximum kinetic energy of the electrons in electron volts.

13. Chapter 2, Atomic Physics 13 Nankai University, CY Li 2012/6/30 Einstein?s explanation For a photoelectron, E=hf . The minimum energy required to pull electrons from inside to outside the metal is called the work function W. W=hf0 If an electron is given an energy E larger than W, it can escape the metal and will have a maximum KE: The radiation causes the metal to emit electrons. The minimum energy required to eject an electron from the surface is called the photoelectric work function. The radiation causes the metal to emit electrons. The minimum energy required to eject an electron from the surface is called the photoelectric work function.

14. Chapter 2, Atomic Physics 14 Nankai University, CY Li 2012/6/30 The Compton effect (Compton scattering) This could be explained when X rays are regards as particles (photons). The collision between a photon and an electron is regarded as an elastic collision. Collisions: when kinetic energy as well as momentum are conserved, the collision is elastic. For a collision with energy loss, it is inelastic. The production of X rays is the exact reverse of the photoelectric effect. Here an electron is being used to produce a photon, in favoring of the particle mode of light. Compton explained and modeled the data by assuming a particle (photon) nature for light and applying conservation of energy and conservation of momentum to the collision between the photon and the electron. The scattered photon has lower energy and therefore a longer wavelength Collisions: when kinetic energy as well as momentum are conserved, the collision is elastic. For a collision with energy loss, it is inelastic. The production of X rays is the exact reverse of the photoelectric effect. Here an electron is being used to produce a photon, in favoring of the particle mode of light. Compton explained and modeled the data by assuming a particle (photon) nature for light and applying conservation of energy and conservation of momentum to the collision between the photon and the electron. The scattered photon has lower energy and therefore a longer wavelength

15. Chapter 2, Atomic Physics 15 Nankai University, CY Li 2012/6/30 Discrete spectra Atoms emit and absorb light only at specific frequencies. Emission lines, Absorption lines, Balmer found that the wavelengths of visible and near ultraviolet line spectra of hydrogen obey a simple formula exactly: RH=1.097x107m-1 is called the Rydberg (???) constant. It was derived from the observations.It was derived from the observations.

16. Chapter 2, Atomic Physics 16 Nankai University, CY Li 2012/6/30 Bohr model There are three postulates used in Bohr?s model: The electron moved in a certain set of stable orbits in which classical mechanics can be used to describe motion of the electron. Moving electrons in stable states (orbits) do not radiate. It radiates when an electron making a transition between the orbits. The orbital angular momenta of the electrons are quantized. A major step was taken by Bohr 1913. He combined the concepts of Rutherfords?s nuclear atom, Planck?s quanta and Einstein?s photons to predict the observed spectrum of atomic hydrogen.A major step was taken by Bohr 1913. He combined the concepts of Rutherfords?s nuclear atom, Planck?s quanta and Einstein?s photons to predict the observed spectrum of atomic hydrogen.

17. Chapter 2, Atomic Physics 17 Nankai University, CY Li 2012/6/30 Quanta in the atom The total energy of the electron is inversely proportional to the square of n, i.e. where n is called quantum number. The total energy is also found to be negative, indicating a ?bound? state. The most negative state, the most tightly bound electron, occurs for n=1, referred to as the ground state of the atom, n>=2, excited states. The angular momentum of the electron moving in a circular orbit can only take discrete values:

18. Chapter 2, Atomic Physics 18 Nankai University, CY Li 2012/6/30 Line spectra of the H atom Energy levels: Lyman series: n=1; Balmer series: n=2; Paschen series: n=3; Brackett series: n=4

19. Chapter 2, Atomic Physics 19 Nankai University, CY Li 2012/6/30 Improvement on the Bohr model Finite nuclear mass (motion of nucleus): When taking the nuclear mass into account, the reduced mass should replace the electron mass. Relativistic correction: The effect of the relativistic mass change m(v) should be considered. Faster?massive?decrease in energy. Sommerfeld?s extension: Electrons should have elliptical orbits with the same energies as that in circular orbits. The second quantum number should be introduced.

20. Chapter 2, Atomic Physics 20 Nankai University, CY Li 2012/6/30 Frank-Hertz experiment Frank & Hertz in 1913 showed the existence of discrete energy levels in atoms. Excitation of quantum jumps by collision.Excitation of quantum jumps by collision.

21. Chapter 2, Atomic Physics 21 Nankai University, CY Li 2012/6/30 Frank-Hertz experiment results Excitation of quantum jumps by collision. As the Franck-Hertz data shows, when the accelerating voltage reaches 4.9 volts, the current sharply drops, indicating the sharp onset of a new phenomenon which takes enough energy away from the electrons that they cannot reach the collector. This drop is attributed to inelastic collisions between the accelerated electrons and atomic electrons in the mercury atoms. The sudden onset suggests that the mercury electrons cannot accept energy until it reaches the threshold for elevating them to an excited state. This 4.9 volt excited state corresponds to a strong line in the ultraviolet emission spectrum of mercury at 254 nm (a 4.9eV photon). Drops in the collected current occur at multiples of 4.9 volts since an accelerated electron which has 4.9 eV of energy removed in a collision can be re-accelerated to produce other such collisions at multiples of 4.9 volts. This experiment was strong confirmation of the idea of quantized atomic energy levels. Excitation of quantum jumps by collision. As the Franck-Hertz data shows, when the accelerating voltage reaches 4.9 volts, the current sharply drops, indicating the sharp onset of a new phenomenon which takes enough energy away from the electrons that they cannot reach the collector. This drop is attributed to inelastic collisions between the accelerated electrons and atomic electrons in the mercury atoms. The sudden onset suggests that the mercury electrons cannot accept energy until it reaches the threshold for elevating them to an excited state. This 4.9 volt excited state corresponds to a strong line in the ultraviolet emission spectrum of mercury at 254 nm (a 4.9eV photon). Drops in the collected current occur at multiples of 4.9 volts since an accelerated electron which has 4.9 eV of energy removed in a collision can be re-accelerated to produce other such collisions at multiples of 4.9 volts. This experiment was strong confirmation of the idea of quantized atomic energy levels.

22. Chapter 2, Atomic Physics 22 Nankai University, CY Li 2012/6/30 Explanation With the increase of grid potential, more electrons move to the plate and the current rises accordingly. For mercury atoms, when V=4.9V, the electrons make inelastic collision and leave the atom jump to a high orbit (n=2). The original electrons move off with little energy and could not reach the plate and thus reduce the current. As V is increased further, the current rises again and would drop at V=9.8V. This would make more atoms to jump to n=2 state. KK-P169KK-P169

23. Chapter 2, Atomic Physics 23 Nankai University, CY Li 2012/6/30 Limitations of Bohr model It can not be generalised to deal with systems with two more electrons as the force between the electrons can not be easily added. It can not explain the closely spaced lines. It can not be used to calculate the rate of transitions between different energy levels. The Bohr model was eventually superseded by the quantum mechanics developed by E Schrodinger, W Heisenberg and others, following the ideas of L de Broglie. Deficiencies of the Bohr model.Deficiencies of the Bohr model.


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