The Schrodinger Equation and What a Wavefunction Says · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

The equation behind every orbital

Science · Chemistry · ages 18-19
Name ______________________   Date ____________

  1. Which quantity tells you where the electron is likely to be found?

    • The square of the wavefunction
    • The sign of the wavefunction
    • The slope of the potential term

  2. What does the time independent equation say about a wavefunction?

    • Its square gives the electric charge of the electron
    • Kinetic plus potential terms acting on it give energy times it
    • It traces the curved path the electron follows

  3. An electron in an atom travels along a definite tiny path.

    Circle one:   True   False

  4. The square of a wavefunction is zero at some point. What does that mean?

    • The electron is never found at that point
    • The electron moves fastest through that point
    • The wavefunction is broken and must be fixed

  5. A proposed wavefunction gives two different values at the same point. What do you conclude?

    • It is fine, since overlapping waves are normal
    • It is acceptable as long as it still fades far away
    • It is rejected, since it must be single valued

  6. Why can a bound electron only have certain energies?

    • Friction removes all the energies in between
    • The nucleus absorbs every energy except a few
    • Only certain wavefunctions satisfy the equation for the system

  7. A candidate is smooth and single valued but grows without limit far from the nucleus. Is it acceptable?

    • No, it must fade to zero far from the nucleus
    • Yes, since growth shows a high energy state
    • Yes, since continuity is the only rule that matters

  8. A student says a wavefunction value of minus 0.3 at a point is impossible, since odds cannot be negative. What is the mistake?

    • Nothing, the student is right about the minus sign
    • The student confused the wavefunction with its square
    • Minus signs are banned everywhere in quantum mechanics
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Answer key

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

The equation behind every orbital W1-mt_WCwbaO9rpR-s1

  1. The square of the wavefunction · Only the square gives odds of finding the electron at each point.
  2. Kinetic plus potential terms acting on it give energy times it · The equation is an energy statement about the wavefunction, not a path.
  3. False · Electrons have no path. A standing wave pattern takes its place.
  4. The electron is never found at that point · Zero square means zero odds. That point is a node.
  5. It is rejected, since it must be single valued · One point, one value. Two values at the same point breaks the rules.
  6. Only certain wavefunctions satisfy the equation for the system · Quantised energies follow from the few waves that fit the system.
  7. No, it must fade to zero far from the nucleus · A bound electron must fade away at large distances, or the odds cannot add to one.
  8. The student confused the wavefunction with its square · A negative wavefunction is fine. Only its square must stay non-negative.
Worksheet · LightMySky