Senior Physics Fall 2014

Week One Summary
Quantum mechanics is the theory that mathematically describes the physics of the very small:
1. Light mostly behaves as a wave, but often we need to think of it as made up of photons – tiny bundles
of energy. The energy of each “packet” depends on the wavelength λ (and hence the color) via the
equation 𝐸 =
ℎ⋅𝑐
𝜆
where h = 6.6 x 10-34 Js and the speed of light c = 3.0 x 108 m/s
2. In any interactions with light, the energy transferred must come from an integer number of photons.
In particular, electrons in atoms can either absorb one full energy packet or none at all. There is no
such thing as half a photon.
3. Photons in the ultraviolet region and above (X-rays, gamma radiation) have enough energy to
completely ionize an atom. If this happens in a living skin cell it has the potential to mutate the DNA
and cause cancer.
4. Photons are massless (have zero rest mass). They can only exist when travelling at light speed. Even
though they have no mass they have momentum. The amount of momentum they carry is given by
𝑝=
ℎ
𝜆
5. Photons hitting a surface impart their momentum to that surface and cause a small but measurable
force. This is sometimes called Radiation Pressure, and can be calculated by

Force = (Number of photons per second) x (photon momentum)
6. Quantum mechanics describes particles as waves. When they are moving they have a wavelength
ℎ
𝑝
given by 𝜆 = .
7. It can be helpful to think of the wave-function as a probability density of where the particle actually
is. However this is not the only interpretation!
8. You cannot know all the information about a given particle at once. In particular measuring a
particles position affects its speed (in an unpredictable way) and measuring its speed changes its
position. There is an inherent uncertainty at the quantum level.
9. Observing a system can also change the system by forcing it into one state or another. An unobserved
particle in an unknown state is described mathematically by a “superposition” of the two possible
states it could be in. Of course if you link the state of the particle to the life of a similarly unobserved
cat, QM says that the cat is both alive and dead until you look at (observe) it.
10. When a particle (an electron for example) encounters a barrier it cannot cross, the wave-function does
not go immediately to zero. If the barrier is thin enough the wave-function can be non-zero on the far
side of the barrier and occasionally the electron can escape. This is called quantum tunneling.
Senior Physics Fall 2014
Week One Summary
Questions
1. Which of the following can and cannot give you skin cancer? PLEASE EXPLAIN YOUR ANSWERS!
a. Going outside without sunblock when the uv index is high
b. Going outside without sunblock when the uv index is medium
c. Sitting all day under a red lamp
d. Standing too near to a microwave oven whose door leaks microwaves
2. A red laser has a wavelength of 600 nm and a power of 1,000 Watts. How much force is felt if that laser
is shone on a black surface that absorbs all of the momentum in the photons?
3. It is thought that shiny solar sails will be more effective than black ones. Why is this?
4. In quantum mechanics to get a value for kinetic energy you use the formula 𝐾𝐸 =
𝑝2
.
2𝑚
Show that this
formula also works in classical physics (hint what is p? what is the classical formula for p and KE?)
5. What thought experiment was used to show the weird nature of the superposition of 2 quantum states?
a. Pavlov’s Dog
b. Schrodinger’s Cat
c. Rutherford’s Mouse
d. The gold leaf experiment
6. The momentum of an electron moving at 250 km/s can be calculated by p = mv. What is the wavelength
of an electron moving this quickly?
h = 6.6 x 10-34 Js
c = 3.0 x 108 m/s
me = 9.1 x 10-31 kg