Quizzes and Exams Physics 223 –001 - Fall 2002

QUIZ #1- 06 September 2002
A glass plate of cross-sectional area 1 meter2 and thickness 0.01 meters is used to separate a region, with a temperature of 40° C on the inside and 0° C on the inside. Determine the energy flowing through the glass plate, in watts.
Note: the thermal conductivity of glass is 1.0 joules/[meter sec °K].

QUIZ #2 - 20 September 2002
 A one mole of a monatomic ideal gas [g=5/3] is contained in a volume of 8 liters at a temperature of 1000 °K, and at initial pressure P0. It undergoes adiabatic expansion until its pressure is reduced to P0/4. Determine the final volume and temperature of the gas, as well as the initial pressure P0, in atmospheres [atm].
Note: R = 8.31 Joules/[mole °K] = 1.99 cal/[mole °K] = 0.0821 liter atm/[mole °K]
QUIZ #3 - 04 October 2002
A plano-convex thin lens, which is flat on the front surface with radius of curvature of 50 cm on the back surface, is made out of transparent material with an index of refraction of 1.6. Determine the focal length of the lens, and determine the location and magnification of any images formed by an object placed 100 cm in front of the front surface of the lens. Are the images upright or inverted; real or virtual? Draw a diagram showing how the images may be obtained by graphical means.
QUIZ #4 -18 October 2002
Light of a certain wavelength l is transmitted through a diffraction grating with 100 lines per millimeter, placed perpendicular to the direction of travel of the beam. A bright spot appears on the screen at an angle of 45° to the screen. Determine the largest wavelength l' that the light can have to produce this spot. With a new beam of light of wavelength l', the bright spot appears at an angle of 46° to the screen. Determine l' - l, the difference in wavelengths.
QUIZ #5 - 01 November 2002
Show that, when a photon of energy E is scattered from a free electron initially at rest, the maximum kinetic energy of the recoiling electron is given by Kmax = E2 / [ E + m c2 /2]
Calculate that maximum recoil energy when the photon has an initial energy of 100 keV.
QUIZ #6 - 06 November 2002
An electron is trapped in a one-dimensional potential well of width 250 pm, in its ground state. How much energy must the electron absorb if it is to jump up to a state with n = 4?
QUIZ #7 - 25 November 2002
An x-ray is emitted from an ionized Krypton [Z=36] atom via a Ka transition, corresponding to an electron moving from the n=2 to n=1 shell. Determine the energy of the emitted x-ray [in electron Volts] and its wavelength [in picometers]
TEST #1 - 07 October 2002

#1. [20 points] The temperature of a 2.00 kg block of copper is increased slowly (reversibly) from 300 °K to 400 °K. The specific heat of copper is 386 joules/(mole °K). Find the heat absorbed by the block and its change in entropy during this process.

#2. [20 points] A fixed amount of an ideal monatomic gas starts at pressure, volume = (P0, V0,T0); point A. It first undergoes an adiabatic expansion to 3 volume 3V0; point B. Then it is heated at constant volume until it reaches its original temperature T0: point C. Finally, it is compressed isothermally [fixed temperature] back to point A. Give the pressure and temperature at points B and C, the net work done in the cycle, and the change in entropy for each of the three processes in the cycle.

#3. [20 points] Suppose that, in the first stage of a two-stage Carnot engine, energy Q1 is absorbed as heat at temperature T1, work W1 is done, and energy Q2 is expelled as heat at a lower temperature T2. The second stage [also a Carnot engine] absorbs the energy Q2 expelled from the first stage, does work W2, and expels energy Q3 at a still lower temperature T3. Determine the total efficiency of this two stage cycle, (W1 + W2)/Q1, in terms of the temperatures. Note that T1 > T2 > T3.

#4. [20 points] Suppose that one of the slits of a double-slit interference experiment is wider than the other, so that the amplitude of the electric field for light from the bottom slit is three times the amplitude of light from the top slit. In terms of the (small) distance d between slits and the (large) distance between the slit and the screen, determine the (relative) intensities of light on the screen. What is the ratio of maximum to minimum intensity?

#5. [20 points] An object is placed in 90 cm directly in front of a converging lens of focal length 60 cm. A mirror is placed 150 cm directly behind the same lens. Determine all images of the system, indicate whether they are real, v, virtual, or upright, and determine the magnification for each image.

#6. [Extra Credit; 10 points] A person looks into a deep pool of water [index of refraction n = 1.33] and sees a large fish. The fish is located at a depth of 5 meters below the horizontal surface of the pool. If the person sees the fish at an angle of 45° to the vertical, determine the apparent depth of the fish in the water, as seen by the person. Draw a diagram showing the path of light traveling from the fish to the person, giving its angles with respect to the vertical as appropriate. [You may take the index of refraction of air as 1.00 for this problem.]

TEST #2 - 13 November 2002

#1. [20 points] A radar system of a navy cruiser transmits at a wavelength of 2.0 cm, from a circular antenna of diameter 2.3 meters. At a range of 10 km, what is the smallest distance that two boats can lie from each other, and still be resolved as separate objects by the radar system?

#2. [20 points] A radio station is broadcasting signals into outer space at a frequency of 1000 kiloHertz. A fast moving rocket ship comes toward the earth at a speed of 60 % of the velocity of light. At what frequency does the rocket ship detect this signal? Note: the velocity of light is c = 3.00 ´  108 meters/second.

#3. [20 points] A photon of energy 7.0 electron Volts strikes a clean metallic surface, which has a work function of 3.0 electron Volts. Determine the maximum velocity of emitted photoelectrons, in meters/second.
Note: h = 6.63 ´  10-34 Joule sec = 1240 eV nm / c; Mass of electron = 9.1 ´  10-31 kg = 510 keV / c2

#4. [20 points] An X-ray of energy 200 keV strikes a free electron in a material. An X-ray is observed to exit at an angle of 90° to the direction of the incident X-ray. Determine the energy of the out-going X-ray, as well as the recoil kinetic energy of the electron, in electron Volts.
Note: h = 6.63 ´  10-34 Joule sec = 1240 eV nm / c; Mass of electron = 9.1 ´  10-31 kg = 510 keV / c2

#5. [20 points] An electron, confined to move freely inside a one- dimensional region of width 1.0 nanometers, lies in its ground state. Determine the probability that the electron lies in the left third of that region.
Note: h = 6.63 ´ 10-34 Joule sec = 1240 eV nm / c;  Mass of electron = 9.1 ´ 10-31 kg = 510 keV / c2

#6. [Extra Credit; 10 points] A particle of mass [rest mass] m has a kinetic energy of motion that is 4 times its rest energy. Calculate the momentum, total energy, and velocity of the particle, as expressed in terms of its mass and the velocity of light.

FINAL EXAM - 09 December 2002

#1. [25 points] A fixed amount of (diatomic) ideal gas undergoes (reversible) adiabatic expansion from a state (Pressure, Volume, Temperature) = (128P0, V0,T0) to a state (P0, VF, TF).

#2. [25 points] A lens of diameter 2.5 cm lies at the front end of a telescope on the roof of the Sears tower, which looks out over Lake Michigan. How far out into the lake [in kilometers] could the telescope resolve a person swimming in the lake, corresponding to an object size of about 2 meters? Use a wavelength of 550 nanometers.

#3. [25 points] A incident projectile, a particle of (rest) mass m and kinetic energy K = 4mc2, is incident upon a target particle of mass m, which is initially at rest. After the (elastic) relativistic collision, the two particles go off in the same direction as that of the incident particle. Determine the momenta of the outgoing particles, expressed in terms of the "natural" momentum scale, mc. Determine the speeds of the particles before and after the collision, expressed in terms of the velocity of light, c.

#4. [25 points] The work function for a clean Potassium surface is 2.25 eV. Determine the maximum kinetic energy of emitted photoelectrons, in electron Volts, if light of wavelength 400 nm is incident upon that surface. What is the maximum speed of these electrons, in meters/second?

#5. [25 points] An x-ray of wavelength 250 pm is emitted via a Ka transition, corresponding to an electron moving from the n=2 to n=1 shell of an ionized atom. Determine the atomic number of the atom in question.

#6. [25 points] A body of mass 50 kilograms is struck by a beam containing a flux of 1010 particles per second for a period of 100 seconds, the particles being g rays [photons] of energy 5 MeV. The energy is fully absorbed in the body.

If the body constitutes a person, what are the prospects for survival?

#7. [Extra Credit; 10 points] Knowing that the minimum x-ray wavelength produced a beam of 40.0 keV x-rays striking a target is 31.1 pm, determine Planck's constant, in electron Volts ´ seconds.