Fermi-Dirac and Bose-Einstein Statistics · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Who may share a quantum seat

Science · Thermal & Statistical Physics · ages 21-22
Name ______________________   Date ____________

  1. How many bosons may occupy a single quantum state?

    • At most one
    • At most two
    • Unlimited sharing is allowed

  2. How many fermions may occupy a single quantum state?

    • At most one
    • At most two
    • As many as arrive

  3. The fermion rule is the exclusion principle in another form.

    Circle one:   True   False

  4. A gas is warmed slightly from absolute zero. What changes in its Fermi-Dirac spread?

    • Only the edge near the step blurs
    • Every deep state empties at once
    • The step moves down to zero energy

  5. What does the Fermi-Dirac spread look like at absolute zero?

    • A gentle slope across all energies
    • A sharp step at the Fermi energy
    • A single tall spike at zero

  6. When is the classical Boltzmann count good enough?

    • When states vastly outnumber particles
    • When every state is fully packed
    • When the temperature reaches absolute zero

  7. A student applies the Boltzmann count to electrons packed shoulder to shoulder. What is wrong?

    • The Boltzmann count only works for photons
    • Dense packing makes sharing common, so quantum rules apply
    • Packed electrons always escape the solid

  8. Two electrons and two photons face three open states. How does the counting differ?

    • The photons get fewer arrangements than the electrons
    • The electrons must pick distinct seats while the photons may share
    • Both pairs are counted in exactly the same way
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Who may share a quantum seat W1-mt_rU5uPV4SB8-s1

  1. Unlimited sharing is allowed · Bosons may crowd into one state without limit.
  2. At most one · One state, one fermion: that is the fermion rule.
  3. True · Both say electrons stack instead of collapsing together.
  4. Only the edge near the step blurs · Deep states stay full; only electrons near the top can move.
  5. A sharp step at the Fermi energy · Full below the Fermi energy, empty above, with a sharp edge.
  6. When states vastly outnumber particles · Plenty of room makes sharing rare, so labels stop mattering.
  7. Dense packing makes sharing common, so quantum rules apply · The classical shortcut needs states to vastly outnumber particles.
  8. The electrons must pick distinct seats while the photons may share · Electrons sit alone; photons may also crowd into one state.
Worksheet · LightMySky