From: Andrew Lorimer Date: Tue, 4 Sep 2018 08:13:06 +0000 (+1000) Subject: finish light matter cheatsheet X-Git-Tag: yr11~48 X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/5728c81e422657961c224e7c9e251b8a3ccaa702?ds=sidebyside;hp=-c finish light matter cheatsheet --- 5728c81e422657961c224e7c9e251b8a3ccaa702 diff --git a/physics/light-matter-ref.md b/physics/light-matter-ref.md index c048891..4d8debb 100644 --- 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 +linestretch: 0.9 --- \pagenumbering{gobble} -\usepackage{multicols} + # Light and Matter ## Planck's equation -$$f={c \over \lambda}$$ - -$$E=hf={hc \over \lambda}$$ +$$f={c \over \lambda},\quad E=hf={hc \over \lambda}=\rho c$$ $$h=6.63 \times 10^{-34}\operatorname{J s}=4.14 \times 10^{-15} \operatorname{eV s}$$ @@ -22,23 +21,25 @@ $$ 1 \operatorname{eV} = 1.6 \times 10^{-19} \operatorname{J}$$ ## 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 -- 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 -### 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 -### 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 @@ -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) -### Stopping potential - -_Smallest voltage to achieve minimum current_ +### Stopping potential ($V$ for minimum $I$) $$V=h_{\text{eV}}(f-f_0)$$ @@ -61,32 +60,36 @@ $$V=h_{\text{eV}}(f-f_0)$$ ## De Broglie's theory $$\lambda = {h \over \rho} = {h \over mv}$$ -$$\rho = {hf \over c} = {h \over \lambda}$$ -$$E = \rho c$$ +$$\rho = {hf \over c} = {h \over \lambda} = mv, \quad E = \rho c$$ -- 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 similar e- and x-ray diff patterns ## 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 - $\Delta E = hf = {hc \over \lambda}$ 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 -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. + + + -$$\sigma E \sigma t \ge {h \over 4 \pi}$$ +$$\sigma \rho \sigma x = {h \over 4\pi}$$ ## 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 -- 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 diff --git a/physics/light-matter-ref.pdf b/physics/light-matter-ref.pdf index 70dc0a6..2492c0a 100644 Binary files a/physics/light-matter-ref.pdf and b/physics/light-matter-ref.pdf differ