Universidad Industrial de Santander – Escuela de Fı́sica

Fı́sica III – Taller 4.

1. Para las caracterı́sticas del efecto foto-eléctrico haga una comparación entre las predecciones teóricas hechas por la mecánica
clásica (usando el modelo ondulatorio) y los resultados experimentales.
2. Which of the following phenomena most demonstrates the wave nature of electrons? photoelectric effect (b) blackbody
radiation Compton effect (d) diffraction of electrons by (e) none of those answers.
3. Which of the following phenomena most clearly demonstrates the particle nature of light? (a) diffraction (b) the photoe-
lectric effect (c) polarization (d) interference (e) refraction. Why?
4. Both an electron and a proton are accelerated to the same speed, and the experimental uncertainty in the speed is the
same for the two particles. The positions of the two particles are also measured. Is the minimum possible uncertainty in
the electron’s position (a) less than the minimum possible uncertainty in the proton’s position, (b) the same as that for
the proton, (c) more than that for the proton, or (d) impossible to tell from the given information?
5. Why was the demonstration of electron diffraction by Davisson and Germer an important experiment?
6. Why is an electron microscope more suitable than an optical microscope for “seeing” objects less than 1 mm in size?
7. The classical model of blackbody radiation given by the Rayleigh–Jeans law has two major flaws. (a) Identify the flaws
and (b) explain how Planck’s law deals with them.
8. Model the tungsten filament of a lightbulb as a black body at temperature 2 900 K. (a) Determine the wavelength of light
it emits most strongly. (b) Explain why the answer to part (a) suggests that more energy from the lightbulb goes into
infrared radiation than into visible light.
9. A pulsed ruby laser emits light at 694.3 nm. For a 14.0-ps pulse containing 3.00 J of energy, find (a) the physical length
of the pulse as it travels through space and (b) the number of photons in it. (c) Assuming that the beam has a circular
cross-section of 0,600 cm diam- eter, find the number of photons per cubic millimeter.
10. A black body at 7 500 K consists of an opening of diameter 0,05 mm, looking into an oven. Find the number of photons
per second escaping the opening and having wavelengths between 500 nm and 501 nm.
11. An isolated copper sphere of radius 5,00 cm, initially uncharged, is illuminated by ultraviolet light of wavelength 200 nm.
The work function for copper is 4,70 eV. What charge does the photoelectric effect induce on the sphere?
12. Lithium, beryllium, and mercury have work functions of 2,30 eV, 3,90 eV, and 4,50 eV, respectively. Light with a wavelength
of 400 nm is incident on each of these metals. (a) Determine which of these metals exhibit the photoelectric effect for this
incident light. Explain your reasoning. (b) Find the maximum kinetic energy for the photoelectrons in each case.
13. X-rays with a wavelength of 120,0 pm undergo Compton scattering. (a) Find the wavelengths of the photons scattered at
angles of 30,0◦ , 60,0◦ , 90,0◦ , 120◦ , 150◦ , and 180◦ . (b) Find the energy of the scattered electron in each case. (c) Which
of the scattering angles provides the electron with the greatest energy? Explain whether you could answer this question
without doing any calculations.
14. In a Compton scattering experiment, a photon is scattered through an angle of 90,0◦ and the electron is set into motion
in a direction at an angle of 20,0◦ to the original direction of the photon. (a) Explain how this information is sufficient to
determine uniquely the wavelength of the scattered photon and (b) find this wavelength.
15. Why is the following situation impossible? After learning about de Broglie’s hypothesis that material particles of momentum
p move as waves with wavelength lambda = h/p, an 80 kg student has grown concerned about being diffracted when passing
through a doorway of width w = 75 cm. Assume significant diffraction occurs when the width of the diffraction aperture
is less than ten times the wavelength of the wave being diffracted. Together with his classmates, the student performs
precision experiments and finds that he does indeed experience measurable diffraction.
16. For
p a free relativistic quantum particle moving with speed u, the total energy of the particle is E = hf = ~ω =
p2 c2 + m2 c4 and the momentum is p = h/λ = ~k = γmu. For the quantum wave representing the particle, the group
speed is vg = dω/dk. Prove that the group speed of the wave is the same as the speed of the particle.
17. Why is the following situation impossible? An air rifle is used to shoot 1,00 g particles at a speed of vx = 100 m/s. The
rifle’s barrel has a diameter of 2,00 mm. The rifle is mounted on a perfectly rigid support so that it is fired in exactly the
same way each time. Because of the uncertainty principle, however, after many firings, the diameter of the spray of pellets
on a paper target is 1,00 cm.