1--- 2geometry: margin=2cm 3columns: 2 4graphics: yes 5author: Andrew Lorimer 6--- 7 8\pagenumbering{gobble} 9\usepackage{multicols} 10 11# Light and Matter 12 13## Planck's equation 14 15$$f={c \over \lambda}$$ 16 17$$E=hf={hc \over \lambda}$$ 18 19$$h=6.63\times 10^{-34}\operatorname{J s}=4.12\times 10^{-15} \operatorname{eV s}$$ 20 21## Force of electrons 22 23$$F=evB$$ 24 25## Photoelectric effect 26 27- $V_{\operatorname{supply}}$ does not affect photocurrent 28- if $V_{\operatorname{supply}} > 0$, e- are attracted to collector anode 29- if $V_{\operatorname{supply}} < 0$, e- are attracted to illuminated cathode, and $I\rightarrow 0$ 30- $v$ of e- depends on ionisation energy (shell) 31 32### Threshold frequency 33- *threshold frequency* $f_0$ - minimum frequency for photoelectrons to be ejected 34- $x$-intercept of frequency vs $E_K$ graph 35- if $f < f_0$, no photoelectrons are detected 36 37### Work function 38- *work function* $\phi$ - minimum energy required to release photoelectrons 39- magnitude of $y$-intercept of frequency vs $E_K$ graph 40- $\phi$ is determined by strength of bonding 41 42$$\phi=hf_0$$ 43 44### Kinetic energy 45 46$$E_{\operatorname{k-max}}=hf - \phi$$ 47 48voltage in circuit = max $E_K$ in eV 49 50### Stopping potential 51 52_Smallest voltage to achieve minimum current_ 53 54$$V_0 = {E_{K \operatorname{max}} \over q_e} = {{hf - \phi} \over q_e}$$ 55 56## De Broglie's theory 57 58$$\lambda = {h \over \rho} = {h \over mv}$$ 59$$\rho = {hf \over c} = {h \over \lambda}$$ 60$$E = \rho c$$ 61 62- 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 ($< r_{\operatorname{proton}}$) 63- confirmed by Davisson and Germer's apparatus (diffraction pattern like double-slit) 64- also confirmed by Thomson - e- diffraction pattern resembles x-ray (wave) pattern 65 66## X-ray and electron interaction 67 68- electron is only stable in orbit if $mvr = n{h \over 2\pi}$ where $n \in \mathbb{Z}$ 69- rearranging this, $2\pi r = n{h \over mv}$ (circumference) 70- if $2\pi r \ne n{h \over mv}$, interference occurs, standing wave cannot be established 71 72## Spectral analysis 73 74<!--  --> 75- $\Delta E = hf = {hc \over \lambda}$ between ground / excited state 76- $f$ of a photon emitted or absorbed can be calculated from energy difference: $E_2 – E_1 = hf$ or $= hc$ 77- Ionisation energy - min $E$ required to remove e- 78- EMR is absorbed/emitted when $E_{\operatorname{K-in}}=\Delta E_{\operatorname{shells}}$ (i.e. $\lambda = {hc \over \Delta E_{\operatorname{shells}}}$) 79 80## Indeterminancy principle 81 82measuring location of an e- requires hitting it with a photon, but this causes $\rho$ to be transferred to electron, moving it. $\therefore, \sigma E \propto {1 \over \sigma t}$ 83 84$$\sigma E \sigma t \ge {h \over 4 \pi}$$ 85 86## Wave-particle duality 87wave model: 88 89- cannot explain photoelectric effect 90- $f$ is irrelevant to photocurrent 91- predicts delay between incidence and ejection 92- speed depends on medium 93 94particle model: 95 96- explains photoelectric effect 97- rate of photoelectron release $\propto$ intensity 98- no time delay - one photon releases one electron 99- 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 100- light exerts force 101- light bent by gravity