Worksheet: De Broglie Wavelengths

In this worksheet, we will practice deriving the de Broglie wavelength and calculating and interpreting its value for particles of known mass and velocity.

Q1:

Calculate the wavelength of an electron traveling at a velocity of 1.000×10 m/s.

  • A 1 . 1 6 × 1 0 m
  • B 7 . 2 7 × 1 0 m
  • C 1 . 3 7 × 1 0 m
  • D 6 . 0 4 × 1 0 m
  • E 3 . 9 6 × 1 0 m

Q2:

What is the de Broglie wavelength of a 100 g baseball traveling at a velocity of 35.0 m/s?

  • A 1 . 8 9 × 1 0 m
  • B 1 . 9 × 1 0 m
  • C 1 . 8 9 × 1 0 m
  • D 1 . 8 9 × 1 0 m
  • E 1 . 8 9 × 1 0 m

Q3:

An electron ()e has a mass of 9.10938×10 kg, and the mass of a proton (p) is 1.67262×10 kg. Assuming the electron and the proton move at the same speed of 300 m/s, which of the following is a true statement concerning the de Broglie wavelengths?

  • A 𝜆 = 1 , 8 3 6 𝜆 p e
  • B 𝜆 = 3 0 0 𝜆 p e
  • C 𝜆 = 3 0 0 𝜆 e p
  • D 𝜆 = 1 , 8 3 6 𝜆 e p

Q4:

Calculate the de Broglie wavelength for an electron moving at a speed of 4.800×10 m/s. Use 9.11×10 kg for the mass of an electron and 6.626×10 J⋅s for the Planck constant.

  • A 1 . 3 8 × 1 0 m
  • B 7 . 2 7 3 × 1 0 m
  • C 1 . 5 2 × 1 0 m
  • D 6 . 6 0 × 1 0 m

Q5:

Calculate the de Broglie wavelength of a 0.1400 kg baseball moving at a speed of 40.00 m/s. Use a value of 6.626×10 for Planck’s constant.

  • A 1 . 6 5 7 × 1 0 m
  • B 4 . 7 3 3 × 1 0 m
  • C 1 . 1 8 3 × 1 0 m
  • D 8 . 4 5 1 × 1 0 m

Q6:

An electron ()e has a mass of 9.10938×10 kg, and the mass of a proton (p) is 1.67262×10 kg. Assuming the electron and the proton move at the same speed of 500 m/s, which of the following is a true statement concerning the de Broglie wavelengths?

  • A 𝜆 > 𝜆 e p
  • B 𝜆 = 𝜆 e p
  • C 𝜆 < 𝜆 e p
  • D 𝜆 + 𝜆 = 5 0 0 e p m

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