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.

  • A2.53Γ—10 Nβ‹…m
  • B2.32Γ—10 Nβ‹…m
  • C2.23Γ—10 Nβ‹…m
  • D2.45Γ—10 Nβ‹…m
  • E2.60Γ—10 Nβ‹…m

Q2:

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

  • A3πœ‡οŒ‘
  • B2πœ‡οŒ‘
  • C√2πœ‡οŒ‘
  • Dπœ‡οŒ‘
  • Eβˆ’πœ‡οŒ‘

Q3:

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

  • A2√3πœ‡οŒ‘
  • B√3πœ‡οŒ‘
  • C6πœ‡οŒ‘
  • D2√6πœ‡οŒ‘
  • E√6πœ‡οŒ‘

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‘.

  • Aπœ‡οŒ‘
  • Bβˆ’3πœ‡οŒ‘
  • C2πœ‡οŒ‘
  • Dβˆ’5πœ‡οŒ‘
  • E4πœ‡οŒ‘

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