Worksheet: The Compton Effect and Photon Momentum

In this worksheet, we will practice describing free electron scattering in the Compton effect and calculating photon momentum and radiation pressure.

Q1:

Find the ratio of the Compton shift of a photon scattered from a free electron at a scattering angle of 30.00 to that of a photon scattered at an angle of 45.00.

Q2:

What is the ratio of the wavelength shift of a photon scattered by a free electron to that of a photon scattered at the same angle by a free proton?

  • A 1 1 , 8 3 6
  • B 1 1 , 5 0 0
  • C 1 1 , 7 0 7
  • D 1 1 , 0 0 0
  • E 1 1 , 3 3 3

Q3:

What is the momentum of a 600 nm wavelength photon?

  • A 3 . 3 1 × 1 0 kg⋅m/s
  • B 1 . 6 5 × 1 0 kg⋅m/s
  • C 2 . 2 0 × 1 0 kg⋅m/s
  • D 3 . 0 0 × 1 0 kg⋅m/s
  • E 1 . 1 0 × 1 0 kg⋅m/s

Q4:

In a beam of white light (wavelengths from 390 to 770 nm), what range of momentum can the photons have?

  • A 3 . 4 0 × 1 0 kg⋅m/s to 8.37×10 kg⋅m/s
  • B 3 . 1 4 × 1 0 kg⋅m/s to 10.3×10 kg⋅m/s
  • C 2 . 2 5 × 1 0 kg⋅m/s to 9.60×10 kg⋅m/s
  • D 1 . 7 0 × 1 0 kg⋅m/s to 8.61×10 kg⋅m/s
  • E 1 . 7 0 × 1 0 kg⋅m/s to 6.81×10 kg⋅m/s

Q5:

Find the wavelength of a photon with a momentum of 3.65×10 kg⋅m/s.

Q6:

Find the energy of a photon with momentum 4.02×10 kg⋅m/s.

  • A 2 . 3 2 × 1 0 J
  • B 2 . 0 1 × 1 0 J
  • C 3 . 0 0 × 1 0 J
  • D 1 . 1 5 × 1 0 J
  • E 1 . 2 1 × 1 0 J

Q7:

A photon has a wavelength of 3.10 μm and an electron has the same momentum as this photon.

Calculate the momentum of the photon.

  • A 2 . 0 5 × 1 0 kg⋅m/s
  • B 2 . 1 4 × 1 0 kg⋅m/s
  • C 3 . 1 7 × 1 0 kg⋅m/s
  • D 4 . 7 2 × 1 0 kg⋅m/s
  • E 3 . 5 8 × 1 0 kg⋅m/s

Find the velocity of the electron.

Find the kinetic energy of the electron.

  • A 1 . 7 8 × 1 0 J
  • B 3 . 7 5 × 1 0 J
  • C 2 . 5 1 × 1 0 J
  • D 1 . 8 5 × 1 0 J
  • E 2 . 3 3 × 1 0 J

Q8:

X-rays of wavelength 9.00 nm are scattered from a block of carbon at angles of 30.0, 90.0, and 180.

What wavelength do the scattered photons have for a 30.0 angle of scattering? Write your answer to six significant figures.

What wavelength do the scattered photons have for a 90.0 angle of scattering? Write your answer to six significant figures.

What wavelength do the scattered photons have for a 180 angle of scattering? Write your answer to six significant figures.

Q9:

A spectrometer with a 2.00 μm wide circular opening is used to measure the wavelengths of the scattered X-rays in the Compton experiment. The width measurement is accurate to 4.99×10 nm. What is the minimum scattering angle at which the X-rays interacting with the free electrons can be distinguished from those interacting with the atoms?

Q10:

A photon of energy 4.98 keV collides with a stationary electron and is scattered at an angle of 58. What is the energy acquired by the electron in the collision?

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