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The dependence of the short wavelength limit λmin\lambda_{min} on the accelerating potential VV is represented by the curve of figure:

A

Curve A

B

Curve B

C

Curve C

D

None of these

Step-by-Step Solution

The short wavelength limit (λmin\lambda_{min}), also known as the cutoff wavelength, for X-rays produced in a tube is determined by the maximum energy of the incident electrons. The entire kinetic energy (K=eVK = eV) of an electron is converted into a single photon of maximum energy (Emax=hνmaxE_{max} = h\nu_{max}). Using the relation E=hcλE = \frac{hc}{\lambda}, we get: eV=hcλmineV = \frac{hc}{\lambda_{min}} λmin=hce1V\lambda_{min} = \frac{hc}{e} \cdot \frac{1}{V}

Since hh, cc, and ee are constants (Source ), λmin\lambda_{min} is inversely proportional to the accelerating potential VV (λmin1/V\lambda_{min} \propto 1/V). The graph representing this inverse relationship is a rectangular hyperbola. Assuming standard graphical representations where curve C depicts a hyperbola (decreasing λ\lambda as VV increases), C is the correct representation.

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