--- /dev/null
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+\@writefile{toc}{\contentsline {section}{\numberline {5}Light and Matter}{}}
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$1 \operatorname{eV} = 1.6 \times 10^{-19} \operatorname{J}$
- eaccelerated with $x$ V is given $x$ eV
+ e- accelerated with $x$ V is given $x$ eV
\[W={1\over2}mv^2=qV \tag{field or points}\]
\[v=\sqrt{{2qV} \over {m}}\tag{velocity of particle}\]
\subsection*{Power transmission}
% \begin{align*}
- $$V_{\operatorname{rms}}={V_{\operatorname{p\rightarrow p}}\over \sqrt{2}}$$
- P_{\operatorname{loss}} = \Delta V I = I^2 R = {{\Delta V^2} \over R} \\
- V_{\operatorname{loss}}=IR
+ \[V_{\operatorname{rms}}={V_{\operatorname{p\rightarrow p}}\over \sqrt{2}} \]
+ \[P_{\operatorname{loss}} = \Delta V I = I^2 R = {{\Delta V^2} \over R} \]
+ \[V_{\operatorname{loss}}=IR \]
% \end{align*}
Use high-$V$ side for correct $|V_{drop}|$
\textbf{nodes:} fixed on graph
\textbf{Longitudinal (motion $||$ wave)}
- \includegraphics[height=4cm]{graphics/longitudinal-waves.png}
+ \includegraphics[width=6cm]{graphics/longitudinal-waves.png}
\textbf{Transverse (motion $\perp$ wave)}
- \includegraphics[height=4cm]{graphics/transverse-waves.png}
+ \includegraphics[width=6cm]{graphics/transverse-waves.png}
% -----------------------
\subsection*{Motors}
$T={1 \over f}\quad$(period: time for one cycle)
- $v=f \lambda \quad$(speed: displacement per second)
+ $v=f \lambda \quad$(speed: displacement / sec)
% -----------------------
\subsection*{Doppler effect}
- When $P_1$ approaches $P_2$, each wave $w_n$ has slightly less distance to travel than $w_{n-1}$. Hence, $w_n$ reaches the observer sooner than $w_{n-1}$, increasing "apparent" wavelength.
+ When $P_1$ approaches $P_2$, each wave $w_n$ has slightly less distance to travel than $w_{n-1}$. $w_n$ reaches observer sooner than $w_{n-1}$ ("apparent" $\lambda$).
% -----------------------
\subsection*{Interference}
% -----------------------
\subsection*{Polarisation}
- \includegraphics[height=4cm]{graphics/polarisation.png}
+ \includegraphics[height=3.5cm]{graphics/polarisation.png}
% -----------------------
\subsection*{Refraction}
- \includegraphics[height=4cm]{graphics/refraction.png}
+ \includegraphics[height=3.5cm]{graphics/refraction.png}
Angle of incidence $\theta_i =$ angle of reflection $\theta_r$
% -----------------------
\subsection*{Planck's equation}
- 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}
-
- 1 \operatorname{eV} = 1.6 \times 10^{-19} \operatorname{J}
+ \[ f={c \over \lambda},\quad E=hf={hc \over \lambda}=\rho c \]
+ \[ h=6.63 \times 10^{-34}\operatorname{J s}=4.14 \times 10^{-15} \operatorname{eV s} \]
+ \[ 1 \operatorname{eV} = 1.6 \times 10^{-19} \operatorname{J} \]
\subsection*{Force of electrons}
- 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}
+ \[ F={2P_{\text{in}}\over c} \]
+ % \begin{align*}
+ \[ \text{photons / sec} = {\text{total energy} \over \text{energy / photon}} \]
+ \[ ={{P_{\text{in}} \lambda} \over hc}={P_{\text{in}} \over hf} \]
+ % ={P_{\text{in}} \lambda} \over hc}={P_{\text{in}} \over hf}
+ % \end{align*}
\subsection*{Photoelectric effect}
\begin{itemize}
\item $V_{\operatorname{supply}}$ does not affect photocurrent
- \item $V_{\operatorname{sup}} > 0$: eattracted to collector anode
+ \item $V_{\operatorname{sup}} > 0$: e- attracted to collector anode
\item $V_{\operatorname{sup}} < 0$: attracted to illuminated cathode, $I\rightarrow 0$
- \item $v$ of edepends on ionisation energy (shell)
+ \item $v$ of depends on ionisation energy (shell)
\item max current depends on intensity
\end{itemize}
$V=h_{\text{eV}}(f-f_0)$
+ \columnbreak
+
\subsection*{De Broglie's theory}
- $\lambda = {h \over \rho} = {h \over mv}$
- $\rho = {hf \over c} = {h \over \lambda} = mv, \quad E = \rho c$
+ \[ \lambda = {h \over \rho} = {h \over mv} \]
+ \[ \rho = {hf \over c} = {h \over \lambda} = mv, \quad E = \rho c \]
\begin{itemize}
\item cannot confirm with double-slit (slit $< r_{\operatorname{proton}}$)
\item confirmed by similar e- and x-ray diff patterns
\subsection*{Spectral analysis}
\begin{itemize}
- $n\item $\Delta E = hf = {hc \over \lambda}$ between ground / excited state
- $n\item $E$ and $f$ of photon: $E_2 - E_1 = hf = {hc \over \lambda}$
- $n\item Ionisation energy - min $E$ required to remove e-
- $n\item EMR is absorbed/emitted when $E_{\operatorname{K-in}}=\Delta E_{\operatorname{shells}}$ (i.e. $\lambda = {hc \over \Delta E_{\operatorname{shells}}}$)
+ \item $\Delta E = hf = {hc \over \lambda}$ between ground / excited state
+ \item $E$ and $f$ of photon: $E_2 - E_1 = hf = {hc \over \lambda}$
+ \item Ionisation energy - min $E$ required to remove e-
+ \item EMR is absorbed/emitted when $E_{\operatorname{K-in}}=\Delta E_{\operatorname{shells}}$ (i.e. $\lambda = {hc \over \Delta E_{\operatorname{shells}}}$)
+ \item No. of lines - include all possible states
\end{itemize}
- \subsection{Indeterminancy principle}
+ \subsection{Uncertainty principle}
measuring location of an e- requires hitting it with a photon, but this causes $\rho$ to be transferred to electron, moving it.
\subsection{Wave-particle duaity}
wave model:
-
- \item cannot explain photoelectric effect
- \item $f$ is irrelevant to photocurrent
- \item predicts delay between incidence and ejection
- \item speed depends on medium
+ \begin{itemize}
+ \item cannot explain photoelectric effect
+ \item $f$ is irrelevant to photocurrent
+ \item predicts delay between incidence and ejection
+ \item speed depends on medium
+ \end{itemize}
particle model:
- \item explains photoelectric effect
- \item rate of photoelectron release $\propto$ intensity
- \item no time delay - one photon releases one electron
- \item 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
- \item light exerts force
- \item light bent by gravity
+ \begin{itemize}
+ \item explains photoelectric effect
+ \item rate of photoelectron release $\propto$ intensity
+ \item no time delay - one photon releases one electron
+ \item 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
+ \item light exerts force
+ \item light bent by gravity
+ \end{itemize}
+
+ % +++++++++++++++++++++++
+ \section{Uncertainty}
+
+ \textbf{Absolute uncertainty} - $\Delta$ - same units as quantity.
+ \[ \Delta(m) = {{\mathcal{E}(m)} \over 100} \cdot m \]
+
+ \[ (A \pm \Delta A) + (B \pm \Delta A) = (A+B) \pm (\Delta A + \Delta B) \]
+ \[ (A \pm \Delta A) - (B \pm \Delta A) = (A-B) \pm (\Delta A + \Delta B) \]
+ \[ c(A \pm \Delta A) = cA \pm c \Delta A \]
+
+ \textbf{Relative uncertainty} - $\mathcal{E}$ - unitless.
+ \[ \mathcal{E}(m) = {{\Delta(m)} \over m} \cdot 100} \]
+ \[ (A \pm \mathcal{E} A) \cdot (B \pm \mathcal{E} B) = (A \cdot B) \pm (\mathcal{E} A + \mathcal{E} B) \]
+ \[ (A \pm \mathcal{E} A) \div (B \pm \mathcal{E} B) = (A \div B) \pm (\mathcal{E} A + \mathcal{E} B) \]
+ \[ (A \pm \mathcal{E} A)^n = (A^n \pm n \mathcal{E} A) \]
+ \[ c(A \pm \mathcal{E} A)=cA \pm \mathcal{E} A \]
+
+ Uncertainty of a measurement is $1 \over 2$ the smallest division
+
+ \textbf{Precision} - concordance of values \\
+ \textbf{Accuracy} - closeness to actual value
+
