## E = pc [ENDORSED]

$\lambda=\frac{h}{p}$

Alexa Pham 1D
Posts: 69
Joined: Wed Sep 30, 2020 10:03 pm

### E = pc

Hi, I know it's only Week 1 and we're reviewing Fundamentals but I was a bit confused what E = pc meant when watching the "Wave Properties of Electrons and The De Broglie Equation" audio-visual focus module. If someone could explain it to me, I'd really appreciate it!

Mikayla Kwok 3K
Posts: 109
Joined: Wed Sep 30, 2020 9:51 pm

### Re: E = pc

Hi! I'm also still trying to grasp the logic behind each value, but here is what I can explain as far as the derivation and use of the formula.

The formula is derived from E=hv (energy = Planck's constant*frequency) and c=[lambda]*v (speed of light = wavelength*frequency). By isolating v in the latter equation and substituting the values into the first, you get E=hc/[lambda] (energy = Planck's constant*speed of light/wavelength). Because De Broglie's equation states [lambda]=h/p (wavelength = Planck's constant/momentum), you can substitute the values of lambda in this equation into E=hc/[lambda]. You would end up with E=hcp/h, or E=pc (energy = momentum*speed of light), because the Planck's constants in the numerator and denominator cancel out.

E=pc is used to calculate the energy of particles that do not have rest masses, like photons. Even though photons do not have rest masses, they do have momentum, which you can find with p=h/[lambda].

Andrew Wang 1C
Posts: 101
Joined: Wed Sep 30, 2020 10:11 pm
Been upvoted: 5 times

### Re: E = pc  [ENDORSED]

Hi there!

E = pc is derived from E = mc2. Since c is the speed of light, we can think of E = mc2 as E = mv2, or E = mvv. And since momentum p = mv, we can plug in momentum to get E = pv. After substituting c back in, we end up with E = pc.

You can connect this with the equation from photoelectric effect, $E = \frac{h}{\lambda}c$. Looking at E = pc and $E = \frac{h}{\lambda}c$ side by side, we see that $p = \frac{h}{\lambda}$, which can be rearranged to de Broglie's equation, $\lambda = \frac{h}{p}$. So what I made of it is that E = pc can be thought of as a "stepping stone" in deriving de Broglie's equation.

Please correct me if I'm wrong, and I hope this helps!