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Step-by-Step Explanation
1. Einstein’s Photoelectric Equation
Einstein’s photoelectric equation states that the maximum kinetic energy of the ejected photoelectrons is given by
$K_{\text{max}} = h \nu - h \nu_0$,
where
$h$ is Planck’s constant,
$\nu$ is the frequency of the incident radiation,
and
$\nu_0$ is the threshold frequency below which no photoelectrons are emitted.
2. Form of the Graph
From the equation
$K_{\text{max}} = h \nu - h \nu_0$,
it is clear that the expression is a straight-line equation of the form
$y = mx - c$,
where:
$K_{\text{max}}$ corresponds to $y$ (the dependent variable).
$\nu$ corresponds to $x$ (the independent variable).
The slope is $h$, which is a constant (Planck’s constant).
The intercept on the $K_{\text{max}}$-axis is $-\,h\,\nu_0$.
Hence, plotting the maximum kinetic energy $K_{\text{max}}$ on the vertical axis against the frequency $\nu$ on the horizontal axis results in a straight line.
3. Key Observations
1. The kinetic energy becomes zero when
$h \nu - h \nu_0 = 0 \implies \nu = \nu_0$.
This indicates that no electrons are emitted below the threshold frequency $\nu_0$.
2. Above $\nu_0$, the kinetic energy increases linearly with frequency.
4. Conclusion
The correct graph, therefore, is a straight line with slope $h$ and intercept
$-\,h\,\nu_0$. This matches the fourth option provided.
