Wave nature of particles and Compton scattering

1. Which of the following experiments gives evidence of the wave nature of particles?

  • A. Diffraction of particles
  • B. The photoelectric effect
  • C. Compton scattering
  • D. The Geiger-Marsden-Rutherford experiment

Q2+3. In an experiment, fast moving electrons of momentum p are directed at a single slit of width x, and then onto a detecting screen. The electrons form a distribution across the screen as shown by this graph.

single slit diffraction pattern

The electrons are spread over a narrow range of angles. The angle from the central peak to the first minimum is θ. What is the value of θ in terms of x and p?

 derived from DL6ER
CC BY-SA 4.0
  • A. ${ph} \over{x}$
  • B. ${h} \over{px}$
  • C. ${px} \over{h}$
  • D. ${xh} \over{p}$

3. The speed of electrons is increased. What will happen to the height h of the central maximum, and the angle θ?

h θ
A
 increases increases
B
 remain constant increases
C
 increases decreases
D
 remain constant decreases

4. Why are interference patterns not typically observed for larger 'macroscopic' particles like molecules?

  • A. The de Broglie wavelength is too large for interference patterns to be observed
  • B. The de Broglie wavelength is too small for interference patterns to be observed
  • C. The de Broglie wavelength formula only holds for very small masses
  • D. Wave-particle duality is not observed for particles heavier than electrons
5. Electrons of mass m and charge e are accelerated from rest across a voltage V. Which of the following expressions gives the subsequent de Brogile wavelength of the electrons?
  • A. $ {h} \over{\sqrt{2meV}}$
  • B. $ {h^2} \over{2meV}$
  • C. $ {h \sqrt{2m \over{eV}}}$
  • D. $ {2mh^2} \over{eV}$

6-10: The following questions are about compton scattering from an electron, as shown in this diagram.

compton scattering diagram EN

The maximum possible change in wavelength Δλ of the photon after collision with an electron is 2.43 pm (picometres).

from work by EoD
CC BY-SA 4.0

6. At what deflection angle θ does the maximum change in wavelength occur, and how does Δλ change if a heavier particle such as a proton causes Compton scattering?

θ for maximum Δλ Δλ for proton
A
 0° increases
B
 0° decreases
C
 90° increases
D
 90° decreases

7. If the angle θ in the diagram above is close to 90°, what is the wavelength of the scattered photon λ' ?
(Original wavelength of photon = λ)

  • A. λ + h/(mc)
  • B. λ - h/(mc)
  • C. λh/(mc)
  • D. zero

8. A photon of wavelength 4.8 pm is incident on a stationary electron. The photon is deflected by 60° in the collision. Given that cos(60°) = 0.5, what is the approximate wavelength of the deflected photon?

  • A. 7.2 pm
  • B. 6.0 pm
  • C. 3.6 pm
  • D. 2.4 pm

9. With reference to the 2-dimensional collision shown in the diagram above, which of the following statements about linear momentum and the total energy are correct?

linear momentum Total Energy
A
 conserved conserved
B
 conserved in the horizontal direction only conserved
C
 conserved not conserved
D
 conserved in the horizontal direction only not conserved

10. The kinetic energy of the the scattered electron is Ee. Which of these statements is correct, assuming the electron was stationary before the collision?

  • A. Ee = hc/λ - hc/λ'
  • B. Ee = hc/λ' - hc/λ
  • C. Ee < hc/λ - hc/λ'
  • D. Ee < hc/λ - hc/λ'