Ideal Quantum Gases and Bose-Einstein Condensation · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

When bosons pile into one state

Science · Thermal & Statistical Physics · ages 22-23
Name ______________________   Date ____________

  1. Below the critical temperature, where sits a finite fraction of atoms?

    • Spread evenly over all states
    • In the single ground state
    • Outside the trap entirely

  2. What does an occupation number tell you?

    • The average headcount of one state
    • The total energy of the gas
    • The critical temperature value

  3. Condensation needs attractive forces between the bosons.

    Circle one:   True   False

  4. Why must the ground state be split off before integrating?

    • It holds a macroscopic share the integral undercounts
    • It has infinite energy
    • Integrals never apply to bosons

  5. Excited states saturate during cooling. Where does the next atom go?

    • Into a hotter state
    • Out of the system
    • Into the ground state

  6. A fermion gas is cooled the same way. Does it condense likewise?

    • Only above the critical temperature
    • Yes, identically to bosons
    • No, one state holds at most one fermion

  7. The same gas is warmed well above the critical temperature. What happens to the condensate fraction?

    • It stays exactly fixed
    • It shrinks away as excited states reopen
    • It moves to the highest state

  8. A student keeps the ground state inside the smooth integral. What goes wrong?

    • The critical temperature doubles
    • The condensate fraction is undercounted
    • Fermions start condensing
LightMySky · lightmysky.comW1-mt_wR2YnShTwJ-s1

Answer key

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

When bosons pile into one state W1-mt_wR2YnShTwJ-s1

  1. In the single ground state · Saturation forces the surplus into the lowest state.
  2. The average headcount of one state · Each state gets its own average fill.
  3. False · Statistics alone drives the pile-up.
  4. It holds a macroscopic share the integral undercounts · One term among many cannot carry a finite fraction.
  5. Into the ground state · Saturation leaves only the ground state open.
  6. No, one state holds at most one fermion · Exclusion blocks the pile-up.
  7. It shrinks away as excited states reopen · Heat lifts atoms back into excited states.
  8. The condensate fraction is undercounted · The integral misses the macroscopic spike.
Worksheet · LightMySky