MODERN PHYSICS

1. Electrons J.J. Thompson Robert Millikan Photons Max Planck Albert Einstein Photoelectric Effect Experiment The Graph Energy Levels Absorption/Emission Spectra Bohr Model De Broglie Wavelength Compton Scattering MODERN PHYSICS Nuclear Notation Energy-Mass Equivalence Nuclear Decay Fission Fusion

2. The Electron in Brief We will mainly deal with Electrons and Photons in this unit. Therefore, We will start with some properties of each particle. 1897: J.J. Thomson Discovered the electron and measured the properties of the particle (the electron). However, his instruments were crude. He could only measure the charge to mass ratio, and not the charge or mass itself.

3. J.J. Thomson’s Experiment In the year 1896 J.J. Thomson conducted an experiment by which he defined the connection of particles charge and its mass – the Charge to Mass ratio (q/m). He turned the cathode ray’s beam on the collector. The beam transferred its charge to the collector and warmed it. He knew collector's mass, its specific heat and the heat gain. He measured the temperature of the collector using a light thermosteam fastened to the collector. He measured the total charge gathered on the collector using a very sensitive electrometer.   He obtained a value of ~ q/m = 1*1011 coulombs per kilogram. Today, the accepted value is 1.768 x1011 coulombs per kilogram

4. The Electron in Brief We will mainly deal with Electrons and Photons in this unit. Therefore, We will start with some properties of each particle. 1897: J.J. Thomson Discovered the electron and measured the properties of the particle (the electron). However, his instruments were crude. He could only measure the charge to mass ratio, and not the charge or mass itself. 1906: Robert Millikan devised an experiment to measure the charge of the electron ( q = -1.6x10-19 C). This experiment is the famous “Millikan Oil Drop Experiment”

5. Millikan Oil Drop Experiment An atomizer sprayed a fine mist of oil droplets into the upper chamber. Some of these tiny droplets fell through a hole in the upper floor into the lower chamber of the apparatus. Millikan first let them fall until they reached terminal velocity due to air resistance. Using the microscope, he measured their terminal velocity and calculated the mass of each oil drop.

6. Millikan Oil Drop Experiment Next, Millikan applied a charge to the falling drops by irradiating the bottom chamber with x-rays. This caused the air to become ionized (air particles lost electrons). A part of the oil droplets captured one or more of those extra electrons and became negatively charged. By attaching a battery to the plates of the lower chamber he created an electric field between the plates that would act on the charged oil drops; he adjusted the voltage untill the electric field force would just balance the force of gravity on a drop, and the drop would hang suspended in mid-air. Some drops have captured more electrons than others, so they will require a higher electrical field to stop.

7. Millikan Oil Drop Experiment When a drop is suspended, its weight  m · g  is exactly equal to the electric force applied, the product of the electric field and the charge q · E.m · g = q · E Millikan then simply solved for q, the charge of the electron: q = (m · g) /E q = -1.6x10-19 C

8. The Electron in Brief We will mainly deal with Electrons and Photons in this unit. Therefore, We will start with some properties of each particle. 1897: J.J. Thompson Discovered the electron and measured the properties of the particle (the electron). However, his instruments were crude. He could only measure the charge to mass ratio, and not the charge or mass itself. 1906: Robert Millikan devised an experiment to measure the charge of the electron ( q = -1.6x10-19 C). This experiment is the famous “Millikan Oil Drop Experiment” With Thompson’s charge to mass ratio, and Millikan’s charge, the mass of the electron could then be calculated: m = 9.11x10-31 kg

9. The Photon blackbody radiation In the late 1800’s scientists had been working a way to describe how hot objects cool by giving off light in various parts of the electromagnetic spectrum. The study of this effect is known as blackbody radiation. Blackbody – An ideal object that emits and absorbs radiation Blackbody Radiation – The electromagnetic radiation given off by a blackbody at a given temperature You have seen blackbody radiation. Any object That is hot enough gives off light (blackbody radiation)

10. The Photon blackbody radiation If an object is hotter than its surroundings it will cool by giving off light. In order to study this effect scientist had to eliminate the other modes of cooling. Blocks of graphite were hollowed and a small hole was drilled into the carbon. Although the outside of the carbon block would cool by convection as well as radiation, the inside would cool by mostly radiation alone. The intensity of each wavelength of light emitted by the inside of the hot, black boxes was studied, hence the name- blackbody radiation.

11. blackbody radiation James Clark Maxwell had discovered the equations that governed the production and transmission of these waves through space and time. A serious problem arose when the electromagnetic spectrum emitted by a radiating body did not match the spectrum that should be produced from the mathematical model of light. The fact that the classical theory did not match the actual spectrum emitted by blackbodies came to be known as the ultra-violet catastrophe. • Classical Model, as Energy increases, the intensity should increase Real Life:

12. blackbody radiation 1900:Max Planck developed a mathematical model that fit the blackbody radiation data without using any known theory. The idea was to find what function worked and then determine what the theory would be. Much to the surprise of Planck, the mathematical model that worked called for light to be jumping off the hot objects in bits and pieces like particles instead of waves.

13. Energy of a photon: In order to avoid the UV catastrophe, Plank discovered light is emitted in Discrete energy units (quanta): E = hf E: the energy f: the frequency of light h: a constant (Planck’s Constant) 6.63x10-34 j s

14. Energy of a photon: E = hf E: the energy f: the frequency of light h: a constant (Planck’s Constant) 6.63x10-34 j s Since Planck’s constant is so small, another way to express It is in terms of the electronvolt (eV). 1 eV is equal to the amount of kinetic energy gained by a single electron when it accelerates through an electric potential difference of one volt. Thus it is 1 volt (1 j/C) multiplied by the electron charge (1.6×10−19 C). Therefore, one electron volt is equal to 1.6×10−19 J h: Planck’s constant = 6.63x10-34 j s = 4.14x10-15 eV s

15. Enter Einstein: 1905: Albert Einstein, while working on his theory of relativity, discovered a few more properties of light. 1. Photons travel at v = c in a vacuum. c = 3x108 m/s

16. Enter Einstein: 1905: Albert Einstein, while working on his theory of relativity, discovered a few more properties of light. 1. Photons travel at v = c in a vacuum. c = 3x108 m/s 2. Although photons are particles, photons have no rest mass (rest mass is the mass of a stationary object) (no rest mass is unique to photons, everything else has a mass)

17. Enter Einstein: 1905: Albert Einstein, while working on his theory of relativity, discovered a few more properties of light. 1. Photons travel at v = c in a vacuum. c = 3x108 m/s 2. Although photons are particles, photons have no rest mass (rest mass is the mass of a stationary object) (no rest mass is unique to photons, everything else has a mass) 3.Although photons do not have mass, they have momentum: p = h /  (p = h /  only applies to photons, for all other objects, use p = mv)

18. Enter Einstein: Momentum of a photon:p = h /  By substituting: E = hf and c = f  , --> E = hc/  --> E = pc Therefore, the energy of a photon can be written as: E = hfE = hc/ E = pc The product of Planck’s constant and the speed of light show up so often that the AP exam will have a value listed in the constants table

19. A 3-milliwatt pen laser radiates at 633 nm. Find values for the following: a) Frequency of light emitted b) energy of a single photon in joules, c) energy of a photon in electron volts d) momentum of a single photon. Example Problem

20. A 3-milliwatt pen laser radiates at 633 nm. Find values for the following: a) Frequency of light emitted, b) energy of a single photon in joules, c) energy of a photon in electron volts, and d) momentum of a single photon Example Problem a) c = f or f = c/ = 3x108m/s / 633x10-9 m f = 4.74x1014 Hz b) E = hf = 6.63x10-34 Jsec (4.74x1014 1/s) E = 3.14x10-19 J c) E = hf = 4.14x10-15 eVs (4.74x1014 1/s) E = 1.96 eV d) p = h/ = 6.63x10-34 Jsec/ 6.33x10-9 m or p = E/c = 3.14x10-19 J / 3x108m/s p = 1.05x10-27 Nsec

21. The Photoelectric Effect Late 1800’s: Heinrich Hertz noticed that under the right conditions UV light could cause sparks to fly from metal surfaces. This phenomenon was labeled the photoelectric effect. photoelectric effect - The emission of electrons from material as a result of light falling on it What did not make sense about the phenomena was that only light above a certain threshold frequency would cause the electrons to be ejected from the surface.  Light below that frequency, regardless of its brightness would not knock electrons off the surface.

22. The Photoelectric Effect Principle observations 1. Electrons are emitted only when the frequency of light is above the threshold value, no matter how intense the light is. 2. Using a setup similar to the one shown below, they found that the KE of the ejected electrons is directly proportional to the frequency of the light hitting the metal surface. 3. It was also discovered that the current in the circuit is proportional to the brightness of the light hitting the metal, but only if the threshold frequency of the metal was exceeded.

23. The Photoelectric Effect Albert Einstein’s Explanation: In 1905 Albert Einstein gave a very simple explanation of the photoelectric effect Light is acting like particles. Each electron can absorb a single photon. When you increase the intensity of light more photons are created and liberate more electrons. This explains the liner relationship between the intensity of the light source and the photocurrent.

24. The Photoelectric Effect Albert Einstein’s Explanation: Einstein’s idea incorporated Planck’s quantum hypothesis into a statement of energy conservation: The energy (hf) of the photon must be equal to the energy needed to free the electron plus the electron's KE KEmax = hf – ф Ф: the Work Function: the energy needed to free the electron. hf: the total energy of the photon.

25. The Photoelectric Effect Albert Einstein’s Explanation: KEmax = hf – ф The minimum energy (the threshold energy required to remove an electron from the surface is easy to calculate, set KE = 0. Therefore, hfth = ф This equation is often solved to find the threshold or cutoff frequency

26. The Photoelectric Effect Albert Einstein’s Explanation: Einstein predicted that every metal should produce a linear graph of the stopping voltage as a function of frequency. And that all of the graphs should have the same slope. The equation for the line is: Y = mx + b Remember: KEmax = hf – ф

27. The Photoelectric Effect Albert Einstein’s Explanation: Slope = h(planck’s constant ) X-intercept = fth(threshold frequency) Y-intercept = -ф(work function)

28. Compton Scattering (Verification that Photons have momentum) 1920’s: Arthur Compton discovered that a photon loses energy when it collides with an object (electron). The momentum was transferred, not as a wave, but just like Billiard balls colliding with each other. The photons were behaving like particles. The photon’s obey the law of conservation of momentum, just like a particle with mass.

29. Compton Scattering The particle with mass gains energy and momentum during the collision and the scattered photon loses energy and momentum. Photons can be scattered in any direction after the collision. The shift in wavelength is dependant on the angle of scattering. The bigger the angle, the greater the loss of energy of the photon.

30. Compton Scattering Classical mechanics: m1v1i + m2v2i = m1v1f + m2v2f

31. Compton Scattering Classical mechanics: m1v1i + m2v2i = m1v1f + m2v2f The set up of the problems are the same as classical mechanics. You just have to use the different momentum equations. Remember, if the particles deflect at angles, you need to break them into the X and Y components. Momentum of a photon: p = h/λ Momentum of an electron: p = mv γ

32. Compton Scattering Fortunately, there are no Compton scattering problems on the AP exam, only questions dealing with the implications of Compton Scattering Main point of Compton Scattering: Compton verified that photon’s obey the law of conservation of momentum, just like a particle with mass.

33. Implications of wave/particle duality on the Atom Einstein showed that many aspects of light can only be predicted if we assume light is a particle. Yet it also acts as a wave (diffraction/interference). This is called the Wave/Particle duality of light. It is both a wave and a particle – or something else that we can only measure as a wave or particle. If light can behave as a particle, can a particle behave as a wave?

34. Implications of wave/particle duality on the Atom So far we showed that many aspects of light can only be predicted if we assume light is a particle. Yet it also acts as a wave (diffraction/interference). This is called the Wave/Particle duality of light. It is both a wave and a particle – or something else that we can only measure as a wave or particle. If light can behave as a particle, can a particle behave as a wave? Yes, De Broglie generalized Einstein's wave/particle duality of a photon. The atom can only be fully explained if we assume it is a wave…

35. Implications of wave/particle duality on the Atom Brief history of the atom 1904: J.J. Thomson – Plum Pudding Model: Based on his discovery of the (-) electron, he hypothesized that the electrons were evenly distributed in a positive substance. (Electrons were the raisins, the pudding was the positive charge) The nucleus had not been discovered yet

36. Implications of wave/particle duality on the Atom Brief history of the atom Ernest Rutherford – Electron Orbit Model: Mass is in the Nucleus, electrons orbit 1911: Rutherford conducted a “Gold Foil” Experiment, where he shot alpha particles through a thin foil of Gold. Almost all of the particles went straight through the gold. However, some were deflected. Based on this information, he concluded that the atom was mostly empty space. Therefore, the mass of the atom was contained mostly in a tiny nucleus, and electrons orbited the nucleus like planets orbiting the sun.

37. Implications of wave/particle duality on the Atom Brief history of the atom Ernest Rutherford’s model did not work! The electrons would slowly spiral into the nucleus every time they gave off energy.

38. Implications of wave/particle duality on the Atom Brief history of the atom Before we go to the next model, we must understand Spectral lines. Spectroscopy: The study of spectra which results in diffracting light into its component colors Spectra is thought of as the fingerprint of matter. Each element has it’s own unique spectrum.

39. Implications of wave/particle duality on the Atom Brief history of the atom Spectroscopy plays a major role in determining the chemical composition of substances. Most of modern chemistry and astronomy depends on spectroscopic analysis of materials. MR spectroscopy of a region of the brain to detect a tumor Spectroscopic data of a galaxy to determine its composition

40. Implications of wave/particle duality on the Atom Brief history of the atom Two types of Spectra: Emission: Series of light lines, each represent a particular wavelength of light. Caused by electrons giving off energy (dropping down an energy level). Absorption: Series of dark lines in a spectrum, each line represents a particular wavelength of light that is absorbed. Caused by electrons accepting energy (moving up an energy level).

41. Implications of wave/particle duality on the Atom Absorption spectra of the Sun: Brief history of the atom

42. Implications of wave/particle duality on the Atom Brief history of the atom Emission and Absorption spectrum

43. Implications of wave/particle duality on the Atom Brief history of the atom Spectroscopy: Physicists could use spectroscopy to determine compositions, temperatures, velocities, etc… of many different object. Charts were made of the spectra of each element. However, no one could determine the exact cause of the spectral lines. According to Rutherford’s model, electrons that gave off continuous energy would spiral into the nucleus of the atom. Another model of the atom had to be made.

44. Implications of wave/particle duality on the Atom Brief history of the atom Neils Bohr– Energy Level Model: 1913: In order to explain line Spectra, Bohr modified Rutherford's model by saying electrons can only have special orbits, and electrons can only jump between these certain orbits (energy levels). In order to jump between orbits, electrons could only accept or give off discrete “quanta” of energy (quantum leaps).

45. Implications of wave/particle duality on the Atom Brief history of the atom Neil's Bohr– Energy Level Model: 1913: In order to explain line Spectra, Bohr modified Rutherford's model by saying electrons can only have special orbits, and electrons can only jump between these certain orbits (energy levels). In order to jump between orbits, electrons could only accept or give off discrete “quanta” of energy (quantum leaps).

46. Implications of wave/particle duality on the Atom Brief history of the atom

47. Implications of wave/particle duality on the Atom Brief history of the atom Energy levels of Bohr’s model of the H atom

48. Implications of wave/particle duality on the Atom Brief history of the atom Energy levels of Bohr’s model of the H atom Energy => hf = Ei - Ef

49. Implications of wave/particle duality on the Atom Brief history of the atom Energy levels of Bohr’s model of the H atom When using this equation E is the energy from Bohr’s Energy level diagram. Make sure E is converted into Joules

50. Implications of wave/particle duality on the Atom Brief history of the atom Problem with Bohr’s model: