Question 165 of 165

An electron beam is accelerated by a potential difference $V$ to hit a metallic target to produce $X-$rays. It produces continuous as well as characteristic $X-$rays. If ${\lambda }_{min}$ is the smallest possible wavelength of $X-$ray in the spectrum, the variation of $\log \left({\lambda }_{min}\right)$ with $\log \left(V\right)$ is correctly represented in :

ABCD

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Answer: (B)

$K.E.=eV$,
$KE=$The kinetic energy of electron

The maximum energy of photon$=K.E.$

$eV=\dfrac{hC}{{\lambda }_{min}}$
$\Rightarrow {\lambda }_{min}V=\dfrac{hC}{e}=constant$

Taken $\log$ in both sides

$\ln \left({\lambda }_{\min }\right)+\ln \left(V\right)=\ln \left(constant\right)$

$\Rightarrow \ln \left({\lambda }_{\min }\right)=-\ln \left(V\right)+\ln (constant)$

$y=-ax+c$ the straight line of negative slope.