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The variation of the stopping potential V0 with the frequency v of the light incident on two different photosensitive M1 and M2
Answers (1)
\documentclass{article}
\usepackage{amsmath}
\usepackage{graphicx}
\begin{document}
\section*{Photoelectric Effect: Variation of Stopping Potential with Frequency}
According to Einstein's photoelectric equation:
\[
eV_0 = h\nu - \phi
\]
Where:
\begin{itemize}
\item \( V_0 \): Stopping potential
\item \( \nu \): Frequency of incident light
\item \( h \): Planck's constant
\item \( \phi \): Work function of the material
\item \( e \): Charge of the electron
\end{itemize}
Rewriting the equation:
\[
V_0 = \frac{h}{e}\nu - \frac{\phi}{e}
\]
This is a linear equation of the form \( V_0 = m\nu + c \), where:
\begin{itemize}
\item Slope \( m = \frac{h}{e} \)
\item Y-intercept \( = -\frac{\phi}{e} \)
\item Threshold frequency \( \nu_0 = \frac{\phi}{h} \) (when \( V_0 = 0 \))
\end{itemize}
\section*{Comparison Between Two Materials: \( M_1 \) and \( M_2 \)}
\begin{itemize}
\item Both materials will have straight-line graphs of \( V_0 \) vs. \( \nu \), with the \textbf{same slope} \( \left( \frac{h}{e} \right) \) since \( h \) and \( e \) are constants.
\item The \textbf{intercepts on the frequency axis} (i.e., threshold frequencies) will differ depending on their work functions.
\item If \( \phi_1 < \phi_2 \), then \( \nu_{0,1} < \nu_{0,2} \). So, material \( M_1 \) will start emitting photoelectrons at a lower frequency.
\end{itemize}
\textbf{Conclusion:}
\begin{itemize}
\item The graph of \( V_0 \) vs. \( \nu \) is a straight line for both materials.
\item The material with a lower work function requires a lower threshold frequency.
\item Both lines are parallel but have different intercepts on the frequency axis.
\end{itemize}
\end{document}
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