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# Nuclear Physics

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1. Nuclear Physics

2. Quantum Physics • Physics on a very small (e.g., atomic) scale is “quantized”. • Quantized phenomena are discontinuous and discrete, and generally very small. • Quantized energy can be thought of as existing in packets of energy of specific size. • Atoms can absorb and emit quanta of energy, but the energy intervals are very tiny, and not all energy levels are “allowed” for a given atom.

3. Light: Ray • We know from geometric optics that light behaves as a ray. This means it travels in a straight line. • When we study ray optics, we ignore the nature of light, and focus on how it behaves when it hits a boundary and reflects or refracts at that boundary.

4. Light: Wave • We will frequently use one equation from wave optics in quantum optics. • c = λf • c: 3 x 108m/s (the speed of light in a vacuum) • λ: wavelength (m) (distance from crest to crest) • f: frequency (Hz or s-1)

5. Light: Particle • Light has a dual nature. In addition to behaving as a wave, it also behaves like a particle. • It has energy and momentum, just like particles do. Particle behavior is pronounced on a very small level, or at very high light energies. • A particle of light is called a “photon”.

6. Photon Energy • The energy of a photon is calculated from it the frequency of the light. • E = hf • E: energy (J or eV) • h: Planck’s constant • 6.625×10-34 J s • 4.14 ×10-15 eV s • f: frequency of light (s-1, Hz)

7. Check • Which has more energy in its photons, a very bright, powerful red laser or a small key-ring red laser? • Which has more energy in its photons, a red laser or a green laser?

8. Electron Volts • The electron-volt is the most useful unit on the atomic level. • If a moving electron is stopped by 1 V of electric potential, we say it has 1 electron-volt (or 1 eV) of kinetic energy. • 1 eV = 1.602×10-19 J

9. Problem • What is the frequency and wavelength of a photon whose energy is 4.0 x 10-19 J?

10. Problem • How many photons are emitted per second by a He-Ne laser that emits 3.0 mW of power at a wavelength of 632.8 nm?

11. Atomic Transitions

12. Energy Levels • This graph shows allowed quantized energy levels in a hypothetical atom. • The more stable states are those in which the atom has lower energy. • The more negative the state, the more stable the atom.

13. Energy Levels • The highest allowed energy is 0.0 eV. Above this level, the atom loses its electron. This level is called the ionization level. • The lowest allowed energy is called the ground state. This is where the atom is most stable. • States between the highest and lowest state are called excited states.

14. Energy Levels • Transitions of the electron within the atom must occur from one allowed energy level to another. • The electron CANNOT EXIST between energy levels.

15. Photon Absorption • When a photon of light is absorbed by an atom, it causes an increase in the energy of the atom. • The photon disappears. • The energy of the atom increases by exactly the amount of energy contained in the photon. • The photon can be absorbed ONLY if it can produce an “allowed” energy increase in the atom.

16. Photon Absorption • When a photon is absorbed, it excites the atom to higher quantum energy state. • The increase in energy of the atom is given by ΔE = hf. 0eV -10eV

17. Absorption Spectra • When an atom absorbs photons, it removes the photons from the white light striking the atom, resulting in dark bands in the spectrum. • Therefore, a spectrum with dark bands in it is called an absorption spectrum.

18. Absorption Spectra • Absorption spectra always involve atoms going up in energy level. 0eV -10eV

19. Photon Emission • When a photon of light is emitted by an atom, it causes a decrease in the energy of the atom. • A photon of light is created. • The energy of the atom decreases by exactly the amount of energy contained in the photon that is emitted. • The photon can be emitted ONLY if it can produce an “allowed” energy decrease in an excited atom.

20. Photon Emission • When a photon is emitted from an atom, the atom drops to lower quantum energy state. • The drop in energy can be computed by ΔE = hf. 0eV -10eV

21. Emission Spectra • When an atom emits photons, it glows! The photons cause bright lines of light in a spectrum. • Therefore, a spectrum with bright bands in it is called an emission spectrum.

22. Emission Spectra • Emission spectra always involve atoms going down in energy level. 0eV -10eV

23. Problem • What is the frequency and wavelength of the light that will cause the atom shown to transition from the ground state to the first excited state? Draw the transition.

24. Problem • What is the longest wavelength of light that when absorbed will cause the atom shown to ionize from the ground state? Draw the transition.

25. Problem • The atom shown is in the second excited state. What frequencies of light are seen in its emission spectrum? Draw the transitions.

26. The Photoelectric Effect

27. Absorption • We’ve seen that if you shine light on atoms, they can absorb photons and increase in energy. • The transition shown is the absorption of an 8.0 eV photon by this atom. • You can use Planck’s equation to calculate the frequency and wavelength of this photon.

28. Extra Energy • Now, suppose a photon with TOO MUCH ENERGY encounters an atom? • If the atom is “photo-active”, a very interesting and useful phenomenon can occur… • This is called the Photoelectric Effect.

29. Photoelectric Effect • Some “photoactive” metals can absorb photons that not only ionize the metal, but give the electron enough kinetic energy to escape from the atom and travel away from it. • The electrons that escape are often called “photoelectrons”. • The binding energy or “work function” is the energy necessary to promote the electron to the ionization level. • The kinetic energy of the electron is the extra energy provided by the photon.

30. Photoelectric Effect • Photon Energy = Work Function + Kinetic Energy • hf = Ф + Kmax • Kmax = hf – Ф • Kmax: Kinetic energy of “photoelectrons” • hf: energy of the photon • Ф : binding energy or “work function” of the metal.

31. Problem • Suppose the maximum wavelength a photon can have and still eject an electron from a metal is 340 nm. What is the work function of the metal surface?

32. Photoelectric Effect • Suppose you collect Kmax and frequency data for a metal at several different frequencies. You then graph Kmax for photoelectrons on y-axis and frequency on x-axis. What information can you get from the slope and intercept of your data?

33. The Photoelectric Effect • The Photoelectric Effect experiment is one of the most famous experiments in modern physics. • The experiment is based on measuring the frequencies of light shining on a metal (which is controlled by the scientist), and measuring the resulting energy of the photoelectrons produced by seeing how much voltage is needed to stop them. • Albert Einstein won the Nobel Prize by explaining the results.

34. Photoelectric Effect Diagram

35. Photoelectric Effect • Voltage necessary to stop electrons is independent of intensity (brightness) of light. It depends only on the light’s frequency (or color). • Photoelectrons are not released below a certain frequency, regardless of intensity of light. • The release of photoelectrons is instantaneous, even in very feeble light, provided the frequency is above the cutoff.

36. Photoelectric Effect • The kinetic energy of photoelectrons can be determined from the voltage (stopping potential) necessary to stop the electron. • If it takes 6.5 Volts to stop the electron, it has 6.5 eV of kinetic energy.

37. Momentum

38. Mass of a Photon • Photons do not have “rest mass”. They must travel at the speed of light, and nothing can travel at the speed of light unless its mass is zero. • A photon has a fixed amount of energy (E = hf). • We can calculate how much mass would have to be destroyed to create a photon (E=mc2).

39. Problem • Calculate the mass that must be destroyed to create a photon of 340nm light.

40. Photon Momenum • Photons do not have “rest mass”, yet they have momentum! This momentum is evident in that, given a large number of photons, they create a pressure. • A photon’s momentum is calculated by

41. Proof of Photon Momentum • Compton scattering • Proof that photons have momentum. • High-energy photons collided with electrons exhibit conservation of momentum. • Work Compton problems just like other conservation of momentum problems • except the momentum of a photon uses a different equation.

42. Problem • What is the momentum of photons that have a wavelength of 620 nm?

43. Problem • What is the frequency of a photon that has the same momentum as an electron with speed 1200 m/s?

44. Matter Waves

45. Matter Waves • Waves act like particles sometimes and particles act like waves sometimes. • This is most easily observed for very energetic photons (gamma or x-Ray) or very tiny particles (elections or nucleons)

46. Energy • A moving particle has kinetic energy • E = K = ½ mv2 • A particle has most of its energy locked up in its mass. • E = mc2 • A photon’s energy is calculated using its frequency • E = hf

47. Momentum • For a particle that is moving • p = mv • For a photon • p = h/λ • Units?

48. Wavelength • For a photon • λ = c/f • For a particle, which has an actual mass, this equation still works • λ = h/p where p = mv • This is referred to as the deBroglie wavelength

49. Matter Wave Proof • Davisson-Germer Experiment • Verified that electrons have wave properties by proving that they diffract. • Electrons were “shone” on a nickel surface and acted like light by diffraction and interference.

50. Problem • What is the wavelength of a 2,200 kg elephant running at 1.2 m/s?