Question

The shortest wavelength present in the X-rays at an accelerating potential of \(50\ \text{kV}\) is:

• A. \(2.5\ \text{\AA}\)
• B. \(3.5\ \text{\AA}\)
• C. \(0.25\ \text{\AA}\)
• D. \(0.35\ \text{\AA}\)

Hint:

For X-rays, \(\lambda_{\min}(\text{\AA})=\frac{12.4}{V(\text{kV})}\).

Answer 1

The Correct Option is C

Concept:
The minimum wavelength of X-rays is given by Duane-Hunt law: \[ \lambda_{\min}=\frac{12.4}{V} \] where \(V\) is in kV and \(\lambda_{\min}\) is in \(\text{\AA}\).

Step 1: Write the given accelerating voltage. \[ V=50\ \text{kV} \]

Step 2: Apply the formula. \[ \lambda_{\min}=\frac{12.4}{50} \] \[ \lambda_{\min}=0.248\ \text{\AA} \] \[ \lambda_{\min}\approx 0.25\ \text{\AA} \] \[ \therefore \text{Correct Answer is (C)} \]