1# Light and matter 2 3## Photoelectric effect 4 5### Planck's equation 6 7$$E=hf,\quad f={c \over \lambda}$$ 8$$\therefore E={hc \over \lambda}$$ 9 10where 11$E$ is energy of a quantum of light (J) 12$f$ is frequency of EM radiation 13$h$ is Planck's constant ($6.63\times 10^{-34}\operatorname{J s}$) 14 15### Electron-volts 16 17$$ 1 \operatorname{eV} = 1.6\times 10^{-19} \operatorname{J}$$ 18 19*Amount of energy an electron gains when it moves through a potential difference of 1V* 20 21- equivalent unit is Joule seconds (e.g. $h$) 22 23### Photoelectric effect 24 25- some metals becomes positively charged when hit with EM radiation 26- this is due to e- being ejected from surface of metal 27- *photocurrent* - flow of e- due to photoelectric effect 28- causes increase in current in a circuit 29- $V_{\operatorname{supply}}$ does not affect photocurrent 30- if $V_{\operatorname{supply}} \gt 0$, e- are attracted to collector anode. 31- if $V_{\operatorname{supply}} \lt 0$, e- are attracted to illuminated cathode, and $I\rightarrow 0$ 32 33#### Wave / particle (quantum) models 34wave model: 35- cannot explain photoelectric effect 36- $f$ is irrelevant to photocurrent 37- predicts that there should be a delay between incidence of radiation and ejection of e- 38 39particle model: 40- explains photoelectric effect 41- rate of photoelectron release is proportional to intensity of incident light 42- shining light on a metal "bombards" it with photons 43- no time delay 44 45#### Work function and threshold frequency 46 47- *threshold frequency* $f_0$ - minimum frequency for photoelectrons to be ejected 48- if $f \lt f_0$, no photoelectrons are detected 49 50- Einstein: energy required to eject photoelectron is constant for each metal 51- *work function* $\phi$ - minimum energy required to release photoelectrons 52- $\phi$ is determined by strength of bonding 53 54$$\phi=hf_0$$ 55 56#### $E_K$ of photoelectrons 57 58$$E_{\operatorname{k-max}}=hf - \phi$$ 59 60where 61$E_k$ is max energy of an emmitted photoelectron 62$f$ is frequency of incident photon (**not** emitted electron) 63$\phi$ is work function ("latent" energy) 64 65Gradient of a frequency-energy graph is equal to $h$ 66y-intercept is equal to $\phi$ 67 68## Wave-particle duality 69 70### Double slit experiment 71Particle 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. 72 73## De Broglie's theory 74- theorised that matter may display both wave- and particle-like properties like light 75- predict wavelength of a particle with $\lambda = {h \over \rho}$ where $\rho = mv$ 76- 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 ($< r_{\operatorname{proton}}$) 77- confirmed by Davisson and Germer's apparatus (diffraction pattern like double-slit) 78- also confirmed by Thomson - e- diffraction pattern resembles x-ray (wave) pattern 79- electron is only stable in orbit if $mvr = n{h \over 2\pi}$ where $n \in \mathbb{Z}$ 80- rearranging this, $2\pi r = n{h \over mv}$ (circumference) 81- therefore, stable orbits are those where circumference = whole number of e- wavelengths 82- if $2\pi r \ne n{h \over mv}$, interference occurs when pattern is looped and standing wave cannot be established 83 84### Photon momentum 85- if a massy particle (e.g. electron) has a wavelength, then anything with a wavelength must have momentum 86- therefore photons have (theoretical) momentum 87- to solve photon momentum, rearrange $\lambda = {h \over mv}$ 88 89## Spectral analysis 90 91 92### Absorption 93- Black lines in spectrum show light not reflected 94 95### Emission 96- Coloured lines show light being ejected from e- shells 97- Energy change between ground / excited state: $\Delta E = hf = {hc \over \lambda}$ 98- Bohr's model describes discrete energy levels 99- Energy is conserved (out = in) 100- Ionisation energy - minimum energy required to remove an electron 101- EMR is absorbed/emitted when $E_{\operatorname{K-in}}=\Delta E_{\operatorname{shells}}$ (i.e. $\lambda = {hc \over \Delta E_{\operatorname{shells}}}$) 102 103## Light sources 104- **incandescent:** <10% efficient, broad spectrum 105- **LED:** semiconducting doped-Si diodes 106- - most electrons in *valence band* (energy level) 107- - provided energy, electrons can jump to *conduction band* and move through Si as current 108- - colour determined by $\Delta E$ between bands (shells), and type of doping 109- **laser:** gas atoms are excited 110- - *popular inversion* - most gas atoms are excited 111- - photons are released if stimulated by another photon of the right wavelength 112- **synchrotron:** - magnetically accelerates electrons 113- - extremely bright 114- - highly polarised 115- - emitted in short pulses 116- - broad spectrum 117 118## Quantum mechanics 119 120 121 122774 abc melbourne