From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Wed, 22 Aug 2018 23:52:02 +0000 (+1000)
Subject: retarding voltage of electrons
X-Git-Tag: yr11~59
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/9740627fac3bbcc7b442821fc1e6d3eafca7273b

retarding voltage of electrons
---

diff --git a/physics/light-matter.md b/physics/light-matter.md
index 940605b..19c50c3 100644
--- a/physics/light-matter.md
+++ b/physics/light-matter.md
@@ -10,7 +10,7 @@ $$\therefore E={hc \over \lambda}$$
 where  
 $E$ is energy of a quantum of light (J)  
 $f$ is frequency of EM radiation  
-$h$ is Planck's constant ($6.63 \times 10^{-34}\operatorname{J s}$)
+$h$ is Planck's constant ($6.63 \times 10^{-34}\operatorname{J s}=4.12 \times 10^{-15} \operatorname{eV s}$)
 
 ### Electron-volts
 
@@ -68,12 +68,18 @@ $\phi$ is work function ("latent" energy)
 Gradient of a frequency-energy graph is equal to $h$  
 y-intercept is equal to $\phi$
 
+#### Stopping potential $V_0$
+$$V_0 = {E_{K \operatorname{max}} \over q_e} = {{hf - \phi} \over q_e}$$
+
 ## Wave-particle duality
 
 ### Double slit experiment
 Particle model allows potential for photons to interact as they pass through slits. However, an interference pattern still appears when a dim light source is used so that only one photon can pass at a time.
 
 ## De Broglie's theory
+
+$$\lambda = {h \over \rho} = {h \over mv}$$
+
 - theorised that matter may display both wave- and particle-like properties like light
 - predict wavelength of a particle with $\lambda = {h \over \rho}$ where $\rho = mv$
 - impossible to confirm de Broglie's theory of matter with double-slit experiment, since wavelengths are much smaller than for light, requiring an equally small slit ($< r_{\operatorname{proton}}$)
@@ -85,6 +91,8 @@ Particle model allows potential for photons to interact as they pass through sli
 - if $2\pi r \ne n{h \over mv}$, interference occurs when pattern is looped and standing wave cannot be established
 
 ### Photon momentum
+
+$$\rho = {hf \over c} = {h \over \lambda}$$
 - if a massy particle (e.g. electron) has a wavelength, then anything with a wavelength must have momentum
 - therefore photons have (theoretical) momentum
 - to solve photon momentum, rearrange $\lambda = {h \over mv}$