retarding voltage of electrons

diff --git a/physics/light-matter.md b/physics/light-matter.md
index a44f583e777e725cad8152aab71389f76dc5413d..19c50c3c6120b822627651b5b2cc750d83be1eef 100644 (file)
--- 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
 
@@ -29,6 +29,7 @@ $$ 1 \operatorname{eV} = 1.6 \times 10^{-19} \operatorname{J}$$
 - $V_{\operatorname{supply}}$ does not affect photocurrent
 - if $V_{\operatorname{supply}} \gt 0$, e- are attracted to collector anode.
 - if $V_{\operatorname{supply}} \lt 0$, e- are attracted to illuminated cathode, and $I\rightarrow 0$
+- not all electrons have the same velocity - depends on ionisation energy (shell)
 
 #### Wave / particle (quantum) models
 wave model:  
@@ -55,7 +56,7 @@ particle model:
 
 $$\phi=hf_0$$
 
-#### $E_K$ of photoelectrons
+#### $E_K$ of photoelectrons (stopping energy)
 
 $$E_{\operatorname{k-max}}=hf - \phi$$
 
@@ -67,12 +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 ($< r_{\operatorname{proton}}$)
@@ -84,6 +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 $\lambda = {h \over mv}$