These Are the Quantum Physics Equations on the AP Physics B Equation Sheet

These are the Quantum Physics Equations on the AP Physics B Equation Sheet E = hf = pc λ = h/p Kmax = hf – φ ΔE = (Δm)c2

There are wonderful stories that go with each of these ideas, but those are told elsewhere, and you’ve been required to read some of them. This page is like a glossary. It is not a substitute for understanding. (By the way, you don’t need complete understanding. You need familiarity. Most of the modern physics problems tend to be about other topics in disguise. The 2002 example mentioned below is a classic example of this.)

Not long after the electromagnetic wave theory of light was constructed, physicists started attempting to use the laws of physics to predict the behaviors of very small, fast- moving things. (The theory of atoms and electrons developed in the late 1800’s/early 1900’s.)

On such small scales, two surprising things happen: 1) light waves start to behave like particles. 2) small-sized matter sometimes behaves like it is made of waves. In fact, we sometimes calculate the “wavelength of an electron”.

The Energy of the Photon: On the small-scale, light will often act like it is made of countable bundles. Each of these bundles is called a photon, and each photon contains an amount of energy proportional to its frequency:

E = hf where experiments show that the value of h is very small (which makes sense, right?). -34 h = 6.63 x 10 Js. h is called Planck’s Constant, named after Max Planck. This constant kept popping up as an important number in many experiments done on very small-scale objects (the sizes of atoms and electrons). The energy of a stream of light is nhf where n is the number of photons. It’s an integer! So now we believe that light’s energy is quantized!! Usually the number n is too large for us to count, so we can’t tell that light energy is quantized. On the large scale, it appears continuous to us. But on the small scale, light is considered to be like countable particles. (Work on the photoelectric effect in the Edline links Quantum Physics 1 and Quantum Physics 2 that I made for you. Here, every photon of incoming light knocks an electron loose from a certain material. It’s one-to-one and countable. This is the essence of solar panels.)

Momentum of a photon: Go read (but don’t solve) 2002 Free Response Problem 7. Do it. You’ll notice the unsurprising idea that a photon could collide with an electron and cause it to move. Doesn’t this mean that the photon is kicking the electron with some momentum? So photons must carry momentum. But they have no mass. So the momentum of a photon cannot possibly equal mv. Well, the rule is different for photons. The momentum of a photon is its energy divided by its speed c:

p = E/c

Exercise: prove that the above definition of p and E = hf can be combined to yield an equation for p that is only in terms of λ and h. The answer is the 2nd equation in the list above.

With the definition of photon momentum and E=hf, you now have information to complete 2002 FR problem 7. Try it. It is a collision problem – basic mechanics – conservation of momentum with these new photon ideas mixed in.

Third Equation in the List Above: I’ve already written about this in the main packet on modern physics. I won’t repeat that here. It’s related to the Photoelectric Effect. It’s a big deal.

Last Equation in the List Above: When a nucleus decays (due to an overcoming of the Strong Force) the total mass of the resulting parts is actually different than the mass of the parent nucleus that decayed in the first place. This seems to violate the law of Conservation of Mass. But thanks to Einstein, we now believe that a loss or gain in mass, Δm, can be converted to a gain or loss of energy, ΔE. So in a nuclear reaction, if the total product mass is less than the mass of the original nucleus, then Δm represents a LOSS in mass, which means the reaction releases a huge amount of energy ΔE. You can see that ΔE is relatively huge, because

ΔE = (Δm)c2 and c is a relatively large number, and it is squared.

The deBroglie Wavelength of Matter: Louis deBroglie hypothesized that matter can sometimes act wavelike, and his deBroglie wavelength is calculated by using typical wave momentum (λ = h/p) in conjunction with the usual definition of momentum for matter, p = mv

λ = h/p = h/(mv) is the deBroglie wavelength for matter

Remember: practice and example is the way to go to be comfortable with using these modern physics expressions. I’ve given you a lot of sample tests. Don’t shy away from the modern questions now. Once familiar, they are often quite simple. At least try them and ask. And remember, all this fuss is for something that is a fun 10% of the exam.