Worksheet: Electron Spin

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In this worksheet, we will practice calculating the difference in potential energy between the spin states of electrons in an atom.

Q1:

What are the possible polar orientations of the spin momentum vector for an electron?

  • Aup 55∘, down 125∘
  • Bup 53∘, down 127∘
  • Cup 50∘, down 130∘
  • Dup 22∘, down 158∘
  • Eup 35∘, down 145∘

Q2:

A hydrogen atom is placed in an external uniform magnetic field of strength 𝐵=200T. Calculate the wavelength of light produced in a transition from a spin up to a spin down state of the atom.

Q3:

Which of the following is the magnitude of the spin momentum of an electron?

  • A 3 4 ℏ
  • B √ 5 2 ℏ
  • C √ 3 2 ℏ
  • D ℏ
  • E 1 √ 2 ℏ

Q4:

A hydrogen atom is placed in an external uniform magnetic field of magnitude 800 T. Calculate the wavelength of light produced in a transition from a spin-up state to a spin-down state of an electron.

Q5:

A ground-state hydrogen atom is placed in a uniform magnetic field and a photon is emitted in the transition from a spin-up to a spin-down state. The wavelength of the photon is 141 μm. What is the strength of the magnetic field?

Q6:

Which of the following are the magnitudes of the resultant spins of the electrons of the elements boron and nitrogen when in the ground state?

  • A √ 3 2 ℏ , √ 1 5 2 ℏ
  • B ℏ , √ 3 2 ℏ
  • C √ 3 2 ℏ , √ 3 2 ℏ
  • D √ 3 2 ℏ , 3 √ 3 2 ℏ
  • E ℏ , √ 1 5 2 ℏ

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