finish light matter cheatsheet

diff --git a/physics/light-matter-ref.md b/physics/light-matter-ref.md
index c0488911067fbce8879b371a6c15bffb4b2b6fd4..4d8debb621d1dbeb9698160e8e90a2294127002c 100644 (file)
--- a/physics/light-matter-ref.md
+++ b/physics/light-matter-ref.md
@@ -3,18 +3,17 @@ geometry: margin=2cm
 columns: 2
 graphics: yes
 author: Andrew Lorimer
 columns: 2
 graphics: yes
 author: Andrew Lorimer

+linestretch: 0.9

 ---
 
 \pagenumbering{gobble}
 ---
 
 \pagenumbering{gobble}

-\usepackage{multicols}
+<!-- \usepackage{multicols} -->

 
 # Light and Matter
 
 ## Planck's equation
 
 
 # Light and Matter
 
 ## Planck's equation
 

-$$f={c \over \lambda}$$
-
-$$E=hf={hc \over \lambda}$$
+$$f={c \over \lambda},\quad E=hf={hc \over \lambda}=\rho c$$

 
 $$h=6.63 \times 10^{-34}\operatorname{J s}=4.14 \times 10^{-15} \operatorname{eV s}$$
 
 
 $$h=6.63 \times 10^{-34}\operatorname{J s}=4.14 \times 10^{-15} \operatorname{eV s}$$
 


@@ -22,23 +21,25 @@ $$ 1 \operatorname{eV} = 1.6 \times 10^{-19} \operatorname{J}$$
 
 ## Force of electrons
 
 
 ## Force of electrons
 

-$$F=evB$$
+$$F={2P_{\text{in}}\over c}$$
+
+$$\text{photons per second}={\text{total energy} \over \text{energy per photon}}={{P_{\text{in}} \lambda} \over hc}={P_{\text{in}} \over hf}$$

 
 ## Photoelectric effect
 
 - $V_{\operatorname{supply}}$ does not affect photocurrent
 
 ## Photoelectric effect
 
 - $V_{\operatorname{supply}}$ does not affect photocurrent

-- if $V_{\operatorname{supply}} > 0$, e- are attracted to collector anode
-- if $V_{\operatorname{supply}} < 0$, e- are attracted to illuminated cathode, and $I\rightarrow 0$
+- $V_{\operatorname{sup}} > 0$: e- attracted to collector anode
+- $V_{\operatorname{sup}} < 0$: attracted to illuminated cathode, $I\rightarrow 0$

 - $v$ of e- depends on ionisation energy (shell)
 - max current depends on intensity
 
 - $v$ of e- depends on ionisation energy (shell)
 - max current depends on intensity
 

-### Threshold frequency
-- *threshold frequency* $f_0$ - minimum frequency for photoelectrons to be ejected
+### Threshold frequency $f_0$
+- minimum $f$ for photoelectrons to be ejected

 - $x$-intercept of frequency vs $E_K$ graph
 - if $f < f_0$, no photoelectrons are detected
 
 - $x$-intercept of frequency vs $E_K$ graph
 - if $f < f_0$, no photoelectrons are detected
 

-### Work function
-- *work function* $\phi$ - minimum energy required to release photoelectrons
+### Work function $\phi$
+- minimum $E$ required to release photoelectrons

 - magnitude of $y$-intercept of frequency vs $E_K$ graph
 - $\phi$ is determined by strength of bonding
 
 - magnitude of $y$-intercept of frequency vs $E_K$ graph
 - $\phi$ is determined by strength of bonding
 


@@ -51,9 +52,7 @@ $$E_{\operatorname{k-max}}=hf - \phi$$
 voltage in circuit or stopping voltage = max $E_K$ in eV  
 equal to $x$-intercept of volts vs current graph (in eV)
 
 voltage in circuit or stopping voltage = max $E_K$ in eV  
 equal to $x$-intercept of volts vs current graph (in eV)
 

-### Stopping potential
-
-_Smallest voltage to achieve minimum current_
+### Stopping potential ($V$ for minimum $I$)

 
 <!-- $$V_0 = {E_{K \operatorname{max}} \over q_e} = {{hf - \phi} \over q_e}$$ -->
 $$V=h_{\text{eV}}(f-f_0)$$
 
 <!-- $$V_0 = {E_{K \operatorname{max}} \over q_e} = {{hf - \phi} \over q_e}$$ -->
 $$V=h_{\text{eV}}(f-f_0)$$


@@ -61,32 +60,36 @@ $$V=h_{\text{eV}}(f-f_0)$$
 ## De Broglie's theory
 
 $$\lambda = {h \over \rho} = {h \over mv}$$
 ## De Broglie's theory
 
 $$\lambda = {h \over \rho} = {h \over mv}$$

-$$\rho = {hf \over c} = {h \over \lambda}$$
-$$E = \rho c$$
+$$\rho = {hf \over c} = {h \over \lambda} = mv, \quad E = \rho c$$

 
 

-- 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 ($< r_{\operatorname{proton}}$)
-- confirmed by Davisson and Germer's apparatus (diffraction pattern like double-slit)
-- also confirmed by Thomson - e- diffraction pattern resembles x-ray (wave) pattern
+- cannot confirm with double-slit (slit $< r_{\operatorname{proton}}$)
+<!-- - confirmed by Davisson and Germer's apparatus (diffraction pattern like double-slit) -->
+- confirmed by similar e- and x-ray diff patterns

 
 ## X-ray and electron interaction
 
 
 ## X-ray and electron interaction
 

-- electron is only stable in orbit if $mvr = n{h \over 2\pi}$ where $n \in \mathbb{Z}$
-- rearranging this, $2\pi r = n{h \over mv}$ (circumference)
-- if $2\pi r \ne n{h \over mv}$, interference occurs, standing wave cannot be established
+- e- is only stable if $mvr = n{h \over 2\pi}$ where $n \in \mathbb{Z}$
+- rearranging this, $2\pi r = n{h \over mv} = n \lambda$ (circumference)
+- if $2\pi r \ne n{h \over mv}$, no standing wave
+- if e- = x-ray diff patterns, $E_{\text{e-}}={\rho^2 \over 2m}={({h \over \lambda})^2 \div 2m}$
+- calculating $h$: $\lambda = {h \over \rho}$

 
 ## Spectral analysis
 
 <!-- ![](graphics/energy-levels.png) -->
 - $\Delta E = hf = {hc \over \lambda}$ between ground / excited state
 
 ## Spectral analysis
 
 <!-- ![](graphics/energy-levels.png) -->
 - $\Delta E = hf = {hc \over \lambda}$ between ground / excited state

-- $f$ of a photon emitted or absorbed can be calculated from energy difference: $E_2 – E_1 = hf$ or $= hc$
+- $E$ and $f$ of photon: $E_2 - E_1 = hf = hc$

 - Ionisation energy - min $E$ required to remove e-
 - EMR is absorbed/emitted when $E_{\operatorname{K-in}}=\Delta E_{\operatorname{shells}}$ (i.e. $\lambda = {hc \over \Delta E_{\operatorname{shells}}}$)
 
 ## Indeterminancy principle
 
 - Ionisation energy - min $E$ required to remove e-
 - EMR is absorbed/emitted when $E_{\operatorname{K-in}}=\Delta E_{\operatorname{shells}}$ (i.e. $\lambda = {hc \over \Delta E_{\operatorname{shells}}}$)
 
 ## Indeterminancy principle
 

-measuring location of an e- requires hitting it with a photon, but this causes $\rho$ to be transferred to electron, moving it. $\therefore, \sigma E \propto {1 \over \sigma t}$
+measuring location of an e- requires hitting it with a photon, but this causes $\rho$ to be transferred to electron, moving it.
+ <!-- $\therefore, \sigma E \propto {1 \over \sigma t}$ -->
+
+<!-- $$\sigma E \sigma t \ge {h \over 4 \pi}$$ -->

 
 

-$$\sigma E \sigma t \ge {h \over 4 \pi}$$
+$$\sigma \rho \sigma x = {h \over 4\pi}$$

 
 ## Wave-particle duality
 wave model:  
 
 ## Wave-particle duality
 wave model:  


@@ -101,6 +104,6 @@ particle model:
 - explains photoelectric effect
 - rate of photoelectron release $\propto$ intensity
 - no time delay - one photon releases one electron
 - explains photoelectric effect
 - rate of photoelectron release $\propto$ intensity
 - no time delay - one photon releases one electron

-- double slit: photons interact as they pass through slits. interference pattern still appears when a dim light source is used so that only one photon can pass at a time
+- double slit: photons interact. interference pattern still appears when a dim light source is used so that only one photon can pass at a time

 - light exerts force
 - light bent by gravity
\ No newline at end of file
 - light exerts force
 - light bent by gravity
\ No newline at end of file

diff --git a/physics/light-matter-ref.pdf b/physics/light-matter-ref.pdf
index 70dc0a68f9f44e242cfe568809ee9e966ca10d25..2492c0a75675951fa435c45ccab8f2d7f6a20347 100644 (file)
Binary files a/physics/light-matter-ref.pdf and b/physics/light-matter-ref.pdf differ