The Free Electron Gas and the Fermi Energy · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

The electron stack inside a metal

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

  1. How many electrons sit in each level of the stack?

    • Two
    • Four
    • Eight

  2. What is the Fermi energy of a metal?

    • The average energy of all its atoms
    • The energy needed to melt it
    • The topmost electron energy at absolute zero

  3. A completely filled band cannot carry an electric current.

    Circle one:   True   False

  4. Why do metal electrons add so little to heat capacity?

    • Electrons cannot absorb energy at all
    • Only the thin skin near the top can be excited
    • Heat flows only through the atomic lattice

  5. Metal A has denser free electrons than metal B. How do their Fermi energies compare?

    • A packs higher than B
    • B packs higher than A
    • Both are always equal

  6. Which band picture conducts electricity?

    • A full band behind a wide gap
    • A partly filled band with free slots
    • Two full bands stacked together

  7. A student claims heating a metal excites every electron equally. What is wrong?

    • Heat cannot reach inside a metal
    • Deep electrons lack nearby empty states to move into
    • Electrons lose their charge when warmed

  8. A level in the stack already holds two electrons. How many more fit in it?

    Answer: ______________

LightMySky · lightmysky.comW1-mt_4oTalBcKpm-s1

Answer key

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

The electron stack inside a metal W1-mt_4oTalBcKpm-s1

  1. Two · Each level takes a spin pair, no more.
  2. The topmost electron energy at absolute zero · Fill from the bottom and the topmost level is the Fermi energy.
  3. True · With no free slots, no electron can shift under a field.
  4. Only the thin skin near the top can be excited · Deep electrons have no empty states nearby, so they sit out.
  5. A packs higher than B · Fermi energy depends only on electron density.
  6. A partly filled band with free slots · Free slots let electrons shift together under a field.
  7. Deep electrons lack nearby empty states to move into · Only electrons near the top have somewhere to go.
  8. 0 · Two per level is full, so no more fit.
Worksheet · LightMySky