## Photoelectric effect
+
+
### Planck's equation
$$E=hf,\quad f={c \over \lambda}$$
where
$E$ is energy of a quantum of light (J)
$f$ is frequency of EM radiation
-$h$ is Planck's constant ($6.63 \times 10^{-34}\operatorname{J s}$)
+$h$ is Planck's constant ($6.63 \times 10^{-34}\operatorname{J s}=4.12 \times 10^{-15} \operatorname{eV s}$)
### Electron-volts
- $V_{\operatorname{supply}}$ does not affect photocurrent
- if $V_{\operatorname{supply}} \gt 0$, e- are attracted to collector anode.
- if $V_{\operatorname{supply}} \lt 0$, e- are attracted to illuminated cathode, and $I\rightarrow 0$
+- not all electrons have the same velocity - depends on ionisation energy (shell)
#### Wave / particle (quantum) models
wave model:
+
- cannot explain photoelectric effect
- $f$ is irrelevant to photocurrent
- predicts that there should be a delay between incidence of radiation and ejection of e-
particle model:
+
- explains photoelectric effect
- rate of photoelectron release is proportional to intensity of incident light
- shining light on a metal "bombards" it with photons
- no time delay
+- one photon releases one electron
#### Work function and threshold frequency
$$\phi=hf_0$$
-#### $E_K$ of photoelectrons
+#### $E_K$ of photoelectrons (stopping energy)
$$E_{\operatorname{k-max}}=hf - \phi$$
$\phi$ is work function ("latent" energy)
Gradient of a frequency-energy graph is equal to $h$
-y-intercept is equal to $\phi$
+y-intercept is equal to $\phi$
+voltage $V$ in circuit is indicative of max kinetic energy in eV
+
+#### Stopping potential $V_0$
+
+Smallest voltage to achieve minimum current
+
+$$V_0 = {E_{K \operatorname{max}} \over q_e} = {{hf - \phi} \over q_e}$$
## Wave-particle duality
Particle 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.
## De Broglie's theory
+
+$$\lambda = {h \over \rho} = {h \over mv}$$
+
- theorised that matter may display both wave- and particle-like properties like light
- predict wavelength of a particle with $\lambda = {h \over \rho}$ where $\rho = mv$
- 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 ($< r_{\operatorname{proton}}$)
- therefore, stable orbits are those where circumference = whole number of e- wavelengths
- if $2\pi r \ne n{h \over mv}$, interference occurs when pattern is looped and standing wave cannot be established
+
+
### Photon momentum
+
+$$\rho = {hf \over c} = {h \over \lambda}$$
- if a massy particle (e.g. electron) has a wavelength, then anything with a wavelength must have momentum
- therefore photons have (theoretical) momentum
- to solve photon momentum, rearrange $\lambda = {h \over mv}$
### Absorption
-- Black lines in spectrum show light not reflected
+- Black lines in spectrum show light not reflected
+- Frequency of a photon emitted or absorbed can be calculated from energy difference: $E_2 – E_1 = hf$ or $= hc$
### Emission
+
+
+
- Coloured lines show light being ejected from e- shells
- Energy change between ground / excited state: $\Delta E = hf = {hc \over \lambda}$
- Bohr's model describes discrete energy levels
- EMR is absorbed/emitted when $E_{\operatorname{K-in}}=\Delta E_{\operatorname{shells}}$ (i.e. $\lambda = {hc \over \Delta E_{\operatorname{shells}}}$)
## Light sources
+
+
+
- **incandescent:** <10% efficient, broad spectrum
- **LED:** semiconducting doped-Si diodes
- - most electrons in *valence band* (energy level)
## Quantum mechanics
+- uncertainty occurs in any measurement
+- inherent physical limit to absolute accuracy of measurements (result of wave-particle duality)
+- interaction between observer and object
+- measuring location of an e- requires hitting it with a photon, but this causes $\rho$ to be transferred to electron, moving it
+
+### Indeterminancy principle
+
+$$\sigma E \sigma t \ge {h \over 4 \pi}$$
+
+where $\sigma n$ is the uncertainty of $n$
+
+**$\sigma E$ and $\sigma t$ are inversely proportional**
+
+Therefore, position and velocity cannot simultaneously be known with 100% certainty.
+
+### Single-slit diffraction
+
+- one photon passes through slit at any time (controlled by intensity)
+- diffraction pattern can be explained by wave front split into wavelets
+- diffraction can be represented as uncertainty of photonic momentum
+
+
+### Comparison with Bohr's model
+
+**Newtonian (deterministic) model** - current $x$ and $v$ are known, so future $x$ can be calculated
+
+**Quantum mechanical model** - electron clouds rather than discrete shells (electrons are not particlces). We can only calculate probability of an electron being observed at a particular position
+
+Newton's and Einsteins models work together
+
+### Photon-electron interaction
+
+When a photon collides with an electron, momentum is transferred to electron.
+
+$$\rho_{\text{photon}}={h \over \lambda}$$
+$$E=\rho c$$
+
+
+
774 abc melbourne
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