Quantum Tunnelling and the Transmission Probability · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Through the wall: tunnelling and its exponential rule

Science · Quantum & Modern Physics · ages 20-21
Name ______________________   Date ____________

  1. An alpha particle lacks the energy to climb the nuclear wall, yet escapes. How?

    • The nucleus lifts it over the rim
    • It tunnels through the nuclear wall
    • Electrons push it out

  2. Three barriers face the same particle. Which leaks the most?

    • Thin, low, light particle
    • Thick, high, heavy particle
    • Thick, low, heavy particle

  3. In a scanning tunnelling microscope, the current barely responds to tip distance.

    Circle one:   True   False

  4. Why can a scanning tunnelling microscope resolve single atoms?

    • Its current swings wildly with tiny distance changes
    • Its tip touches each atom
    • Its lens magnifies atoms optically

  5. A barrier's width is halved with everything else fixed. What happens to transmission?

    • It roughly doubles
    • It stays about the same
    • It jumps by orders of magnitude

  6. An electron and a proton face identical barriers. Who tunnels better?

    • Equal rates for both
    • The proton
    • The electron, far more readily

  7. A student says tunnelling breaks energy conservation, since the particle crosses a taller barrier. What is the error?

    • Energy is conserved: the wave leaks across with total E unchanged
    • Energy is borrowed and never repaid
    • Barriers lower themselves for quantum particles

  8. Nuclei with slightly thicker walls show vastly longer half-lives. Why?

    • Thicker walls add only a small linear delay
    • Transmission falls exponentially with width
    • Alpha particles slow down inside
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Answer key

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

Through the wall: tunnelling and its exponential rule W1-mt_tLdPJKx8Id-s1

  1. It tunnels through the nuclear wall · Alpha decay is tunnelling out of the nuclear potential.
  2. Thin, low, light particle · Thin, low, and light all favour crossing under the triple test.
  3. False · The current swings wildly with distance, which is what maps atoms.
  4. Its current swings wildly with tiny distance changes · Exponential sensitivity turns sub-atom height shifts into readable current swings.
  5. It jumps by orders of magnitude · Exponential dependence turns a halving into a huge multiplication.
  6. The electron, far more readily · Heavier means weaker, so the light electron wins by far.
  7. Energy is conserved: the wave leaks across with total E unchanged · The particle never owns extra energy inside; it arrives with the same total E.
  8. Transmission falls exponentially with width · A small width change multiplies the escape rate hugely, stretching half-lives.
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