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\includegraphics[height=3.5cm]{graphics/refraction.png} @@ -438,57 +447,72 @@ % ={P_{\text{in}} \lambda} \over hc}={P_{\text{in}} \over hf} % \end{align*} + \subsection*{De Broglie's theory} + + \[ \lambda = {h \over \rho} = {h \over mv} \] + \[ \rho = {hf \over c} = {h \over \lambda} = mv, \quad E = \rho c \] + \begin{itemize} + \item cannot confirm with double-slit (slit $< r_{\operatorname{proton}}$) + \item confirmed by e- and x-ray patterns + \end{itemize} + + \subsection*{X-ray electron interaction} + + \begin{itemize} + \item e- stable if $mvr = n{h \over 2\pi}$ where $n \in \mathbb{Z}$ + \item $\therefore 2\pi r = n{h \over mv} = n \lambda$ (circumference) + \item if $2\pi r \ne n{h \over mv}$, no standing wave + \item if e- = x-ray diff patterns, $E_{\text{e-}}={\rho^2 \over 2m}={({h \over \lambda})^2 \div 2m}$ + % \item calculating $h$: $\lambda = {h \over \rho}$ + \end{itemize} + \subsection*{Photoelectric effect} \begin{itemize} \item $V_{\operatorname{supply}}$ does not affect photocurrent - \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 depends on ionisation energy (shell) + \item $V_{\operatorname{sup}} > 0$: attracted to +ve + \item $V_{\operatorname{sup}} < 0$: attracted to -ve, $I\rightarrow 0$ + \item $v$ of e- depends on shell \item max current depends on intensity \end{itemize} - \textbf{Threshold frequency $f_0$} + \subsubsection*{Threshold frequency $f_0$} - Minimum $f$ for photoelectrons to be ejected. $x$-intercept of frequency vs $E_K$ graph. if $f < f_0$, no photoelectrons are detected. + min $f$ for photoelectron release. if $f < f_0$, no photoelectrons. - \textbf{Work function $\phi$} + \subsubsection*{Work function $\phi=hf_0$} - Minimum $E$ required to release photoelectrons. Magnitude of $y$-intercept of $f$ vs $E_K$ graph. $\phi$ is determined by strength of bonding. Units: eV or J. + min $E$ for photoelectron release. determined by strength of bonding. Units: eV or J. - $\phi=hf_0$ + \subsubsection*{Kinetic energy E_K=hf - \phi = qV_0} - \textbf{Kinetic energy} - E_{\operatorname{k-max}}=hf - \phi + $V_0 = E_K$ in eV \\ + % $E_K = x$-int of $V\cdot I$ graph (in eV) \\ + dashed line below $E_K=0$ - voltage in circuit or stopping voltage = max $E_K$ in eV \\ - $E_K = x$-int of $V\cdot I$ graph (in eV) \\ - dashed line below $E_K=0$ ($E_K < 0$ is impossible) + \subsubsection*{Stopping potential $V_0$ for min $I$} - \textbf{Stopping potential $V$ for min $I$} + $$V_0=h_{\text{eV}}(f-f_0)$$ - $V=h_{\text{eV}}(f-f_0)$ + \subsubsection*{Graph features} - \subsection*{De Broglie's theory} + \newcolumntype{b}{>{\hsize=.75\hsize}X} +\newcolumntype{s}{>{\hsize=.3\hsize}X} - \[ \lambda = {h \over \rho} = {h \over mv} \] - \[ \rho = {hf \over c} = {h \over \lambda} = mv, \quad E = \rho c \] - \begin{itemize} - \item cannot confirm with double-slit (slit $< r_{\operatorname{proton}}$) - \item confirmed by similar e- and x-ray diff patterns - \end{itemize} + \begin{tabularx}{\columnwidth}{bbbb} +\hline +&$m$&$x$-int&$y$-int \\ +\hline +\hline +$f \cdot E_K$ & $h$ & $f_0$ & $-\phi$ \\ +$V \cdot I$ & & $V_0$ & intensity\\ +$f \cdot V$ & ${h \over q}$ & $f_0$ & $-\phi \over q$ & +\hline +\end{tabularx} - \subsection*{X-ray electron interaction} - \begin{itemize} - \item e- is only stable if $mvr = n{h \over 2\pi}$ where $n \in \mathbb{Z}$ - \item rearranging this, $2\pi r = n{h \over mv} = n \lambda$ (circumference) - \item if $2\pi r \ne n{h \over mv}$, no standing wave - \item if e- = x-ray diff patterns, $E_{\text{e-}}={\rho^2 \over 2m}={({h \over \lambda})^2 \div 2m}$ - \item calculating $h$: $\lambda = {h \over \rho}$ - \end{itemize} \subsection*{Spectral analysis} @@ -512,6 +536,7 @@ \item $f$ is irrelevant to photocurrent \item predicts delay between incidence and ejection \item speed depends on medium + \item supported by bright spot in centre \end{itemize} \subsubsection*{particle model} -- 2.43.2