Worksheet: Electron Orbital Magnetic Dipole Moment

In this worksheet, we will practice calculating the magnetic dipole moment of atomic electrons from the spectroscopic description of their quantum states.

Q1:

Find the magnitude of the minimum torque that acts on the orbital magnetic dipole of a 3𝑝 electron in an external magnetic field of 2.50Γ—10 T.

  • A 2 . 5 3 Γ— 1 0    Nβ‹…m
  • B 2 . 3 2 Γ— 1 0    Nβ‹…m
  • C 2 . 2 3 Γ— 1 0    Nβ‹…m
  • D 2 . 4 5 Γ— 1 0    Nβ‹…m
  • E 2 . 6 0 Γ— 1 0    Nβ‹…m

Q2:

In terms of πœ‡οŒ‘, which of the following is the magnitude of an electron magnetic moment?

  • A 3 πœ‡ 
  • B 2 πœ‡ 
  • C √ 2 πœ‡ 
  • D πœ‡ 
  • E βˆ’ πœ‡ 

Q3:

Which of the following is the magnitude of the orbital magnetic dipole moment of the electron in the 3𝑑 state?

  • A 2 √ 3 πœ‡ 
  • B √ 3 πœ‡ 
  • C 6 πœ‡ 
  • D 2 √ 6 πœ‡ 
  • E √ 6 πœ‡ 

Q4:

An electron in a hydrogen atom is in the 𝑛=4, 𝑙=3 state.

Find the smallest angle the electron’s magnetic moment makes with the atom’s 𝑧-axis. Answer to the nearest degree.

Which of the following is the projection of the electron’s magnetic moment at the smallest angle that the moment makes with the atom’s 𝑧-axis? Express your answer in terms of πœ‡οŒ‘.

  • A πœ‡ 
  • B βˆ’ 3 πœ‡ 
  • C 2 πœ‡ 
  • D βˆ’ 5 πœ‡ 
  • E 4 πœ‡ 

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