The dependence of the short wavelength limit | vedclass

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(A) The short wavelength limit $\lambda _{\min }$ is given by the relation $\lambda _{\min } = \frac{hc}{eV}$.Taking the logarithm on both sides,we ge

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$A$

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(A) The short wavelength limit $\lambda _{\min }$ is given by the relation $\lambda _{\min } = \frac{hc}{eV}$.Taking the logarithm on both sides,we get $\log \lambda _{\min } = \log \left( \frac{hc}{e} \right) - \log V$.This can be rewritten as $\log \lambda _{\min } = - \log V + \log \left( \frac{hc}{e} \right)$.This is an equation of a straight line of the form $y = mx + c$,where $y = \log \lambda _{\min }$,$x = \log V$,slope $m = -1$,and intercept $c = \log \left( \frac{hc}{e} \right)$.Since the slope is negative,the graph is a straight line with a downward slope,which corresponds to curve $A$ in the figure.

The dependence of the short wavelength limit $\lambda _{\min }$ on the accelerating potential $V$ is represented by the curve of figure.

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