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In an X-ray tube operating at voltage V, the cut-off (minimum) wavelength is lambda0. If the operating voltage is increased slightly by delta_V, which of the following statements is correct?
- lambda0 changes by +lambda0 * delta_V / V
- lambda0 changes by -lambda0 * delta_V / V
- lambda0 - lambda_Kalpha changes by -lambda0 * delta_V / V
- lambda_Kalpha - lambda0 does not change
Correct answer: lambda0 - lambda_Kalpha changes by -lambda0 * delta_V / V
Solution
lambda0 = hc/(eV), so delta_lambda0 = -(lambda0/V)*delta_V (negative since lambda0 decreases as V increases). lambda_Kalpha is fixed by atomic energy levels. Therefore lambda0 - lambda_Kalpha changes by delta_lambda0 = -lambda0*delta_V/V. The option stating lambda_Kalpha - lambda0 does not change is wrong because lambda0 itself changes.
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