UNIT V MODERN PHYSICS. Updated April 4, 2011 A. P. PHYSICS 1

UNIT V MODERN PHYSICS Updated April 4, 2011 A. P. PHYSICS 1 SPANGLER 3/19/2014

ATOMIC PHYSICS and QUANTUM EFFECTS A. P. PHYSICS 2 SPANGLER 3/19/2014

A. P. PHYSICS 3 SPANGLER 3/19/2014

2010 # 7. Light of wavelength 400 nm is incident on a metal surface, as shown. Electrons are ejected from the metal surface with a maximum kinetic energy of 1.1 x 10-19 J A. P. PHYSICS 5 SPANGLER 3/19/2014

(a) Calculate the frequency of the incoming light. (b) Calculate the work function of the metal surface. (c) Calculate the stopping potential for the emitted electrons. (d) Calculate the momentum of an electron with the maximum kinetic energy. A. P. PHYSICS 6 SPANGLER 3/19/2014

09 #7 A photon of wavelength 250 nm ejects an electron from a metal. The ejected electron has a de Broglie wavelength of 0.85 nm. (a) Calculate the kinetic energy of the electron. (b) Assuming that the kinetic energy found in (a) is the maximum kinetic energy that it could have. calculate the work function of the metal. A. P. PHYSICS 10 SPANGLER 3/19/2014

(c) The incident photon was created when an atom underwent an electronic transition. On the energy level diagram of the atom below, the transition labeled X corresponds to a photon wavelength of 400 nm. Indicate which transition could be the source of the original 250 nm photon by circling the correct letter. Justify your answer. A. P. PHYSICS 11 SPANGLER 3/19/2014

a. A. P. PHYSICS 12 SPANGLER 3/19/2014

b. A. P. PHYSICS 13 SPANGLER 3/19/2014

c. A. P. PHYSICS 14 SPANGLER 3/19/2014

2008 #7 In an electron microscope, a tungsten cathode with work function 4.5 ev is heated to release electrons that are then initially at rest just outside the cathode. The electrons are accelerated by a potential difference to create beam of electrons with a de Broglie wavelength of 0.038 nm. Assume nonrelativistic equations apply to the motion of the electrons. A. P. PHYSICS 15 SPANGLER 3/19/2014

(a) Calculate the momentum of an electron in the beam, in kgm/s. (b) Calculate the kinetic energy of an electron in the beam, in joules. (c) Calculate the accelerating voltage. (d) Suppose that light, instead of heat, is used to release the electrons from the cathode. What minimum frequency of light is needed to accomplish this? A. P. PHYSICS 16 SPANGLER 3/19/2014

SCORING GUIDELINES A. P. PHYSICS 17 SPANGLER 3/19/2014

1 Pt 1 Pt A. P. PHYSICS 18 SPANGLER 3/19/2014

1 Pt 1 Pt 1 Pt A. P. PHYSICS 19 SPANGLER 3/19/2014

1 Pt 1 Pt 1 Pt A. P. PHYSICS 20 SPANGLER 3/19/2014

2007 #7 It is possible for an electron and a positron to orbit around their stationary center of mass until they annihilate each other, creating two photons of equal energy moving in opposite directions. A positron is a particle that has the same mass as an electron and equal but opposite charge. The amount of kinetic energy of the electron- positron pair before annihilation is negligible compared to the energy of the photons created. A. P. PHYSICS 21 SPANGLER 3/19/2014

(a) Calculate, in ev, the rest energy of a positron. (b) Determine, in ev, the energy each emitted photon must have. (c) Calculate the wavelength of each created photon. (d) Calculate the magnitude of the momentum of each photon. (e) Determine the total momentum of the two-photon system. A. P. PHYSICS 22 SPANGLER 3/19/2014

E) Total momentum is zero 1 point A. P. PHYSICS 26 SPANGLER 3/19/2014

2006 #6 A photon with a wavelength of 1.5 x 10-8 m is emitted from an ultraviolet source into a vacuum. (a) Calculate the energy of the photon. (b) Calculate the de Broglie wavelength of an electron with kinetic energy equal to the energy of the photon. (c) Describe an experiment that illustrates the wave properties of this electron. A. P. PHYSICS 27 SPANGLER 3/19/2014

(c) 3 points The expected answer is a description of an experiment in which a beam of electrons is aimed at either a single slit, a double slit, a diffraction grating, or a crystal. The student must also describe the interference pattern of maxima and minima appearing on a screen as evidence of the wave nature of the electron. For using a beam of electrons (NOT a single electron) 1 pt For aiming the electron beam at one of the objects noted above 1 pt For indicating that the resultant is an interference pattern (a drawing was acceptable) 1pt Notes: If the experiment description is completely correct except that it includes a beam of light instead of electrons, it earned two of the three possible points. No points were earned for merely naming an experiment, either in reference to commonly known experimenters ( Davisson Germer experiment ) or pieces of equipment ( doubleslit experiment ). A. P. PHYSICS 30 SPANGLER 3/19/2014

2005 #7 10 Points Total A. P. PHYSICS 31 SPANGLER 3/19/2014

The diagram above shows the lowest four discrete energy levels of an atom. An electron in the n = 4 state makes a transition to the n = 2 state, emitting a photon of wavelength 121.9 nm. (a) Calculate the energy level of the n = 4 state. (b) Calculate the momentum of the photon. A. P. PHYSICS 32 SPANGLER 3/19/2014

The photon is then incident on a silver surface in a photoelectric experiment, and the surface emits an electron with maximum possible kinetic energy. The work function of silver is 4.7 ev. (c) Calculate the kinetic energy, in ev, of the emitted electron. (d) Determine the stopping potential, V S for the emitted electron. A. P. PHYSICS 33 SPANGLER 3/19/2014

SCORING GUIDELINES (a) 4 points For a correct calculation of the photon frequency. 1 pt f = c/λ = (3x 10 8 m/s)/(1.219 x 10-7 m) = 2.46 x 10 15 Hz For correct calculation of the photon energy in electron-volts or joules. 1 pt E ph = hf = (4.14 x10-15 ev s)(2.46 x 10 15 Hz) = 10.2 ev or 1.63 x 10-18 J The two points above were also awarded for correctly using E = hc/λ or using E = pc and the answer from part (b). For indicating that the photon energy is the 1 pt difference between the two energy levels. E 4 =E 2 +E ph =-13.6 ev+10.2 ev =-3.4 ev = -5.44x10-19 J For the correct numerical answer 1 pt A. P. PHYSICS 34 SPANGLER 3/19/2014

Alternate solution Alternate points For use of energy levels and the Bohr model 1 pt E n =E 1 /n 2 For identifying the ground state energy E 1 = 54.4 ev For using the correct quantum number n=4 For the correct answer E 4 = 3.4 ev 1 pt 1 pt 1 pt A. P. PHYSICS 35 SPANGLER 3/19/2014

(b) 2 points p = h/λ or p = E/c For substitution of appropriate values into either of the above equations. p = (6.63 x 10-34 Js) / (121.9 x 10-9 m) or p = (1.63 x 10-18 J) / (3.00 x 10 8 m/s) For the correct answer with correct units p = 5.44 x 10-27 kgm/s (or 3.40 x 10-8 evs/m) 1 pt 1 pt A. P. PHYSICS 36 SPANGLER 3/19/2014

(c) 2 points KE max = E ph - φ For correct substitution of photon energy from part (a), or a calculation of it. 1 pt KEmax = 10.2 ev - 4.7 ev For the correct answer in ev 1 pt KE max = 5.5 ev A. P. PHYSICS 37 SPANGLER 3/19/2014

(d) 2 points KE max = W = qv For using the definition of an ev as the work required to move a charge e through a 1 volt potential difference. 1 pt For the correct answer with units of volts. 1 pt V = 5.5 V Alternate solution Alternate points For understanding the relationship between electrical potential and energy. 1 pt V = KE max /q V = (5.5 ev)(1.6 x 10-19 J/eV)/(1.6 x 10-19 C) = 5.5 V For the correct answer with units of volts. 1 pt A. P. PHYSICS 38 SPANGLER 3/19/2014

04 #6 10 points A student performs a photoelectric effect experiment in which light of various frequencies is incident on a photosensitive metal plate. This plate, a second metal plate, and a power supply are connected in a circuit, which also contains two meters, M1 and M2, as shown. The student shines light of a specific wavelength λ onto the plate. The voltage on the power supply is then adjusted until there is no more current in the circuit, and this voltage is recorded as the stopping potential V. The student then repeats the experiment several more times with different wavelengths of light. The data, along with other values calculated from it, are recorded in the following table. A. P. PHYSICS 39 SPANGLER 3/19/2014

(a) Indicate which meter is used as an ammeter and which meter is used as a voltmeter by checking the appropriate spaces below. M1 M2 Ammeter Voltmeter (b) Use the data above to plot a graph of KE max versus f on the axes below, and sketch a best-fit line through the data. A. P. PHYSICS 40 SPANGLER 3/19/2014

(c) Use the best-fit line you sketched in part (b) to calculate an experimental value for Planck s constant. (d) If the student had used a different metal with a larger work function, how would the graph you sketched in part (b) be different? Explain your reasoning. A. P. PHYSICS 41 SPANGLER 3/19/2014

1 Pt 1 Pt A. P. PHYSICS 43 SPANGLER 3/19/2014

2003 #7 The electron gives away 20.61 ev, but it takes 20.66 ev to raise the neon atom to the higher level - therefore we need another 0.05 ev of energy. The kinetic energy of the neon must equal at least 0.05 ev. (0.5)(4 U x 1.66 x 10-27 kg/u)(v 2 ) = 0.05 ev = 8.0 x 10-21 J v = 2(8 x 10 21 ) =1550 m/s -27 6.644 x 10 A. P. PHYSICS 46 SPANGLER 3/19/2014

λ = h/p = 6.63 x 10-34 J-s / (6.644 x 10-27 kg)(1550 m/s) λ = 6.44 x 10-11 m A. P. PHYSICS 47 SPANGLER 3/19/2014

E = hf = hc/λ λ= hc/ E = (4.14 x 10-15 )(3 x 10 8 )/(20.66 ev - 18.7 ev) λ = 6.33 x 10-7 m A. P. PHYSICS 48 SPANGLER 3/19/2014

E pulse = Pt = 0.01 J E photon = 20.66 18.7 = 1.96 ev = 3.136 x 10-19 J # photons = E pulse /E photon = 3.19 x 10 16 photons A. P. PHYSICS 49 SPANGLER 3/19/2014

2002 #7 A photon of wavelength 2.0 x 10-11 m strikes a free electron of mass m e that is initially at rest, as shown. After the collision, the photon is shifted in wavelength by an amount λ=2h/m e c, and reversed in direction, as shown. A. P. PHYSICS 50 SPANGLER 3/19/2014

(a) Determine the energy in joules of the incident photon. (b) Determine the magnitude of the momentum of the incident photon. (c) Indicate below whether the photon wavelength is increased or decreased by the interaction. Increased Decreased Explain your reasoning. (d) Determine the magnitude of the momentum acquired by the electron. A. P. PHYSICS 51 SPANGLER 3/19/2014

SCORING GUIDELINES a) E = hf = hc/λ E=(6.63x10-34 )(3x10 8 ) / (2 x 10-11 ) = 9.95x10-15 J b) p = h/λ p = (6.63x10-34 )/(2 x 10-11 ) = 3.32 x 10-23 kgm/s c) Increased, must lose energy, must lower frequency, same velocity, c, so λ must increase (v = fλ) A. P. PHYSICS 52 SPANGLER 3/19/2014

d) p of electron = - p of photon λ new = λ + λ = 2x10-11 m + (2)(6.63x10-34 )/(9.11x10-31 )(3x10 8 ) λ new = 2.49 x 10-11 m p = h/λ - h/λ new = 3.32 x 10-23 - 2.66 x 10-23 p = 6.57 x 10-24 kgm/s A. P. PHYSICS 53 SPANGLER 3/19/2014

2000 #5 A sodium photoelectric surface with work function 2.3 ev is illuminated by electromagnetic radiation and emits electrons. The electrons travel toward a negatively charged cathode and complete the circuit shown. The potential difference supplied by the power supply is increased, and when it reaches 4.5 V, no electrons reach the cathode. A. P. PHYSICS 54 SPANGLER 3/19/2014

(a) For the electrons emitted from the sodium surface, calculate the following. i. The maximum kinetic energy ii. The speed at this maximum kinetic energy (b) Calculate the wavelength of the radiation that is incident on the sodium surface. (c) Calculate the minimum frequency of light that will cause photoemission from this sodium surface. A. P. PHYSICS 56 SPANGLER 3/19/2014

SCORING GUIDELINES ai A. P. PHYSICS 57 SPANGLER 3/19/2014

97 #6 A monatomic gas is illuminated with visible light of wavelength 400 nm. The gas is observed to absorb some of the light and subsequently to emit visible light at both 400 nm and 600 nm. A. P. PHYSICS 61 SPANGLER 3/19/2014

(a) In the box below, complete an energy level diagram that would be consistent with these observations. Indicate and label the observed absorption and emissions. A. P. PHYSICS 62 SPANGLER 3/19/2014

b. If the initial state of the atoms has energy -5.0 ev, what is the energy of the state to which the atoms were excited by the 400 nm light? A. P. PHYSICS 64 SPANGLER 3/19/2014

(c) At which other wavelengths outside the visible range do these atoms emit radiation after they are excited by the 400 nm light? A. P. PHYSICS 65 SPANGLER 3/19/2014

SCORING GUIDELINES For drawing one or more energy levels (horizontal lines) between 0 ev and -5 ev (required to earn further points) 1 point For an arrow showing an upward transition from -5 ev to an inserted level For an arrow showing a downward transition opposite to the one above (i.e. these two represent the absorbed and emitted 400 nm light) For a third arrow showing another downward transition, of longer wavelength (smaller energy difference) than the pair above (i.e. representing the 600 nm light) 1 point Either of the two transitions shown is correct. No deductions were made for showing additional transitions. 1 Pt 1 pt 1 point A. P. PHYSICS 66 SPANGLER 3/19/2014

95 #4 A free electron with negligible kinetic energy is captured by a stationary proton to form an excited state of the hydrogen atom. During this process a photon of energy E is emitted, a followed shortly by another photon of energy 10.2 electron volts. No further photons are emitted. The ionization energy of hydrogen is 13.6 ev. A. P. PHYSICS 68 SPANGLER 3/19/2014

(a) Determine the wavelength of the 10.2 ev photon. (b) Determine the following for the 1st photon emitted: i. The energy E of the photon. a ii. The frequency that corresponds to this energy. A. P. PHYSICS 69 SPANGLER 3/19/2014

(c) The following diagram shows some of the energy levels of the hydrogen atom, including those that are involved in the processes described above. Draw arrows on the diagram showing only the transitions involved in these processes. A. P. PHYSICS 70 SPANGLER 3/19/2014

(d) The atom is in its ground state when a 15 ev photon interacts with it. All the photon's energy is transferred to the electron, freeing it from the atom. Determine the following. i. The kinetic energy of the ejected electron. ii. The de Broglie wavelength of the electron. A. P. PHYSICS 72 SPANGLER 3/19/2014

94 #3 A series of measurements were taken of the maximum kinetic energy of photoelectrons emitted from a metallic surface when light of various frequencies is incident on the surface. (a) The following table lists the measurements that were taken. On the axes below, plot the kinetic energy versus light frequency for the five data points given. Draw on the graph the line that is your estimate of the best straight line fit to the data points. A. P. PHYSICS 78 SPANGLER 3/19/2014

(b) From this experiment, determine a value of Planck's constant h in units of electron volt-seconds. Briefly explain how you did this. A. P. PHYSICS 80 SPANGLER 3/19/2014

93 #6 In the x-ray tube shown, a potential difference of 70,000 volts is applied across the two electrodes. Electrons emitted from the cathode are accelerated to the anode, where x-rays are produced. a. Determine the maximum frequency of the x-rays produced by the tube. b. Determine the maximum momentum of the x-ray photons produced. A. P. PHYSICS 84 SPANGLER 3/19/2014

An x-ray photon of the maximum energy produced by this tube leaves the tube and collides elastically with an electron at rest. The frequency of the scattered x-ray photon is 1.64 x 10 19 hertz. A. P. PHYSICS 86 SPANGLER 3/19/2014

As a result, the electron recoils and the x-ray is scattered. A. P. PHYSICS 87 SPANGLER 3/19/2014

c. Determine the kinetic energy of the recoiled electron. d. Determine the magnitude of the momentum of the recoiled electron. A. P. PHYSICS 88 SPANGLER 3/19/2014

92 #4 The ground state energy of a hypothetical atom is at -10.0 ev. When these atoms, in the ground state, are illuminated with light, only the wavelengths of 207 nm and 146 nm are absorbed by the atoms. (a) Calculate the energies of the photons of light of the two absorption-spectrum wavelengths. (b) Complete the energy-level diagram shown for these atoms by showing all the excited energy states. A. P. PHYSICS 96 SPANGLER 3/19/2014

(c) Show by arrows on the energy-level diagram all of the possible transitions that would produce emission spectrum lines. (d) What would be the wavelength of the emission line corresponding to the transition from the second excited state to the first excited state? (e) Would the emission line in (d) be visible? Briefly justify your answer. A. P. PHYSICS 98 SPANGLER 3/19/2014

90 #5 In a television picture tube, electrons are accelerated from rest through a potential difference of 12,000 volts and move toward the screen of the tube. When the electrons strike the screen, x-ray photons are emitted. A. P. PHYSICS 104 SPANGLER 3/19/2014

Determine: (a) The speed of an electron just before it strikes the screen. (b) The number of electrons arriving at the screen per second if the flow of electrons in the tube is 0.01 coulomb per second. A. P. PHYSICS 105 SPANGLER 3/19/2014

An x-ray of maximum energy is produced when an electron striking the screen gives up all of its kinetic energy. For such x-rays, determine: (c) The frequency (d) The wavelength (e) The photon momentum A. P. PHYSICS 106 SPANGLER 3/19/2014

88 #6 Electromagnetic radiation is incident on the surface S of a material as shown. Photoelectrons are emitted from the surface S only for radiation of wavelength 5,000 angstroms or less. It is found that for a certain ultraviolet wavelength, which is unknown, a potential V s of 3 volts is necessary to stop the photoelectrons from reaching the anode A, thus eliminating the photoelectric current. A. P. PHYSICS 109 SPANGLER 3/19/2014

a. Determine the frequency of the 5,000 Å radiation. b. Determine the work function for the material. c. Determine the energy of the photons associated with the unknown wavelength d. Determine the unknown wavelength. A. P. PHYSICS 111 SPANGLER 3/19/2014

NUCLEAR PHYSICS A. P. PHYSICS 115 SPANGLER 3/19/2014

01 #7 Consider the following nuclear fusion reaction that uses deuterium, 2 1H as fuel. 2 4 3( H) He+ H+ 1 2 1 a. Determine the mass defect, given the following information in AMU, u. 2 1 H= 2.0141 He= 4.0026 H= 1.0078 n= 1.0087 1 1 0 n A. P. PHYSICS 116 SPANGLER 3/19/2014

b. Determine the energy in Joules released during a single fusion reaction. c. The United States requires about 10 20 J per year to meet its energy needs. How many deuterium atoms would be necessary to provide this magnitude of energy? A. P. PHYSICS 117 SPANGLER 3/19/2014

d. Assume that 0.015% of the hydrogen atoms in seawater (H 2 0) are deuterium. The atomic mass number of oxygen is 16. About how many kilograms of seawater would be needed per year to provide the hydrogen fuel for fusion reactors to meet the energy needs of the United States? A. P. PHYSICS 118 SPANGLER 3/19/2014

99 #4 part a & b removed The bismuth isotope decays into thallium by emitting an alpha particle according to the following equation: 212 Bi Tl + 83 α A. P. PHYSICS 123 SPANGLER 3/19/2014

c. Determine the atomic number Z and the mass number A of the thallium nuclei produced and enter your answers in the spaces provided below. Z= A= d. The mass of the alpha particle is 6.64 x 10-27 kg. Its measured kinetic energy is 6.09 MeV and its speed is much less than the speed of light. A. P. PHYSICS 124 SPANGLER 3/19/2014

i. Determine the momentum of the alpha particle. ii. Determine the kinetic energy of the recoiling thalliun, nucleus. e. Determine, the total energy released during the decay of 1 mole of bismuth 212. A. P. PHYSICS 125 SPANGLER 3/19/2014

1 Pt 1 Pt 1 Pt 1 Pt A. P. PHYSICS 127 SPANGLER 3/19/2014

96 #5 An unstable nucleus that is initially at rest decays into a nucleus of fermium 252 containing 100 protons and 152 neutrons and an alpha particle that has a kinetic energy of 8.42 MeV. The atomic masses of helium 4 and fermium 252 are 4.00260 u and 252.08249 u, respectively. a. What is the atomic number of the original unstable nucleus? b. What is the velocity of the alpha particle? A. P. PHYSICS 130 SPANGLER 3/19/2014

(c) Where does the kinetic energy of the alpha particle come from? Explain briefly. (d) Suppose that the fermium 252 nucleus could undergo a decay in which a β - particle was produced. How would this affect the atomic number of the nucleus? Explain A. P. PHYSICS 131 SPANGLER 3/19/2014

SCORING GUIDELINES a. A. P. PHYSICS 132 SPANGLER 3/19/2014

91 #5 A polonium nucleus of atomic number 84 and mass number 210 decays to a nucleus of lead by the emission of an alpha particle of mass 4.0026 atomic mass units and kinetic energy 5.5 MeV. (a) Determine each of the following. i. The atomic number of the lead nucleus. ii. The mass number of the lead nucleus. A. P. PHYSICS 136 SPANGLER 3/19/2014

(b) Determine the mass difference between the polonium nucleus and the lead nucleus, taking into account the kinetic energy of the alpha particle but ignoring the recoil energy of the lead nucleus. (c) Determine the speed of the alpha particle. A. P. PHYSICS 137 SPANGLER 3/19/2014

(d) Determine the De Broglie wavelength of the alpha particle. (e) The alpha particle is scattered from a gold nucleus (atomic number 79) in a "headon" collision. Write an equation, but do not solve, that could be used to determine the distance of closest approach of the alpha particle to the gold nucleus. A. P. PHYSICS 138 SPANGLER 3/19/2014

SCORING GUIDELINES (a) A. P. PHYSICS 139 SPANGLER 3/19/2014

89 #6 A lithium nucleus, while at rest, decays into a helium nucleus of rest mass 6.6483 x 10-27 kg and a proton of rest mass 1.6726 x 10-27 kg, as shown by the following reaction. 5 4 2 Li He+ 3 1 1 H In this reaction, momentum and total energy are conserved. After the decay, the proton moves with a speed of 1.95 x 10 7 m/s. A. P. PHYSICS 142 SPANGLER 3/19/2014

a. Determine the kinetic energy of the proton. b. Determine the speed of the helium nucleus. A. P. PHYSICS 143 SPANGLER 3/19/2014

c. Determine the kinetic energy of the helium nucleus. d. Determine the mass that is transformed into kinetic energy in this decay. e. Determine the rest mass of the lithium nucleus. A. P. PHYSICS 144 SPANGLER 3/19/2014