A trapped wave can only sing some notes

Science · Quantum & Modern Physics · ages 19-20

Name ______________________ Date ____________

The second level of the well is four times the ground energy.
Circle one: True False
Why does the infinite well give discrete energies?
- An extra rule bans middle energies
- Boundary conditions fit only some waves
- Friction settles the particle down
How many nodes does the n equals 3 wave have inside?
- Zero
- Two
- Three
The well width is halved. What happens to the ground energy?
- It halves
- It stays the same
- It quadruples
A boxed proton has E1 of 2.05 MeV. Give E2 in MeV.
Answer: ______________
The proton drops from E2 to E1. What carries the difference?
- An emitted photon of E2 minus E1
- A new wall inside the well
- A slower proton mass
E1 is 0.5 eV. Give the photon energy for the drop from E2 to E1 in eV.
Answer: ______________
A student sketches the n equals 2 state as a single hump with no node.
Circle one: True False

Answer key

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

True · Energies scale as n squared, and 2 squared is 4.
Boundary conditions fit only some waves · Zero at both walls admits only whole half-waves.
Two · Three lobes are split by two interior nodes.
It quadruples · Energy scales as one over width squared.
8.2 · E2 is 4 times E1, and 4 times 2.05 is 8.2.
An emitted photon of E2 minus E1 · Energy conservation moves the gap into a photon.
1.5 · Gap is 4 E1 minus E1, which is 3 times 0.5.
False · Two lobes need one central node between them.