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(A) The minimum wavelength (cut-off wavelength) of the continuous $X$-ray spectrum is given by the formula: $\lambda_{\min} = \frac{hc}{eV} = \frac{12

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$0.25 \ \mathring{A}$

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(A) The minimum wavelength (cut-off wavelength) of the continuous $X$-ray spectrum is given by the formula: $\lambda_{\min} = \frac{hc}{eV} = \frac{12400 \ 	ext{eV} \cdot \mathring{A}}{V 	ext{ (in volts)}}$.Substituting the given potential difference $V = 40,000 \ V$:$\lambda_{\min} = \frac{12400}{40000} \ \mathring{A} = 0.31 \ \mathring{A}$.Since the $X$-ray tube cannot produce wavelengths shorter than the cut-off wavelength $\lambda_{\min}$,any wavelength $\lambda Among the given options,$0.25 \ \mathring{A}$ is less than $0.31 \ \mathring{A}$.Therefore,the wavelength $0.25 \ \mathring{A}$ is absent.

When a beam of accelerated electrons hits a target,a continuous $X$-ray spectrum is emitted from the target. Which of the following wavelengths is absent in the $X$-ray spectrum,if the $X$-ray tube is operating at $40,000 \ V$?

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