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$$h=6.63\times 10^{-34}\operatorname{J s}=4.14\times 10^{-15} \operatorname{eV s}$$ 20 21$$ 1 \operatorname{eV} = 1.6\times 10^{-19} \operatorname{J}$$ 22 23## Force of electrons 24 25$$F=evB$$ 26 27## Photoelectric effect 28 29- $V_{\operatorname{supply}}$ does not affect photocurrent 30- if $V_{\operatorname{supply}} > 0$, e- are attracted to collector anode 31- if $V_{\operatorname{supply}} < 0$, e- are attracted to illuminated cathode, and $I\rightarrow 0$ 32- $v$ of e- depends on ionisation energy (shell) 33- max current depends on intensity 34 35### Threshold frequency 36- *threshold frequency* $f_0$ - minimum frequency for photoelectrons to be ejected 37- $x$-intercept of frequency vs $E_K$ graph 38- if $f < f_0$, no photoelectrons are detected 39 40### Work function 41- *work function* $\phi$ - minimum energy required to release photoelectrons 42- magnitude of $y$-intercept of frequency vs $E_K$ graph 43- $\phi$ is determined by strength of bonding 44 45$$\phi=hf_0$$ 46 47### Kinetic energy 48 49$$E_{\operatorname{k-max}}=hf - \phi$$ 50 51voltage in circuit or stopping voltage = max $E_K$ in eV 52equal to $x$-intercept of volts vs current graph (in eV) 53 54### Stopping potential 55 56_Smallest voltage to achieve minimum current_ 57 58<!-- $$V_0 = {E_{K \operatorname{max}} \over q_e} = {{hf - \phi} \over q_e}$$ --> 59$$V=h_{\text{eV}}(f-f_0)$$ 60 61## De Broglie's theory 62 63$$\lambda = {h \over \rho} = {h \over mv}$$ 64$$\rho = {hf \over c} = {h \over \lambda}$$ 65$$E = \rho c$$ 66 67- 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 ($< r_{\operatorname{proton}}$) 68- confirmed by Davisson and Germer's apparatus (diffraction pattern like double-slit) 69- also confirmed by Thomson - e- diffraction pattern resembles x-ray (wave) pattern 70 71## X-ray and electron interaction 72 73- electron is only stable in orbit if $mvr = n{h \over 2\pi}$ where $n \in \mathbb{Z}$ 74- rearranging this, $2\pi r = n{h \over mv}$ (circumference) 75- if $2\pi r \ne n{h \over mv}$, interference occurs, standing wave cannot be established 76 77## Spectral analysis 78 79<!--  --> 80- $\Delta E = hf = {hc \over \lambda}$ between ground / excited state 81- $f$ of a photon emitted or absorbed can be calculated from energy difference: $E_2 – E_1 = hf$ or $= hc$ 82- Ionisation energy - min $E$ required to remove e- 83- EMR is absorbed/emitted when $E_{\operatorname{K-in}}=\Delta E_{\operatorname{shells}}$ (i.e. $\lambda = {hc \over \Delta E_{\operatorname{shells}}}$) 84 85## Indeterminancy principle 86 87measuring location of an e- requires hitting it with a photon, but this causes $\rho$ to be transferred to electron, moving it. $\therefore, \sigma E \propto {1 \over \sigma t}$ 88 89$$\sigma E \sigma t \ge {h \over 4 \pi}$$ 90 91## Wave-particle duality 92wave model: 93 94- cannot explain photoelectric effect 95- $f$ is irrelevant to photocurrent 96- predicts delay between incidence and ejection 97- speed depends on medium 98 99particle model: 100 101- explains photoelectric effect 102- rate of photoelectron release $\propto$ intensity 103- no time delay - one photon releases one electron 104- 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 105- light exerts force 106- light bent by gravity