Step 1: Formula for Cut-off Wavelength (Duane-Hunt Law).
The minimum wavelength (\(\lambda_{min}\)) produced by an X-ray tube operating at voltage \(V\) is given by:
\[ \lambda_{min} = \frac{hc}{eV} \]
Using the shortcut value \(hc \approx 12400 \, \text{eV \AA} \) or \(1240 \, \text{eV nm}\).
Step 2: Calculation.
Given Voltage \(V = 20 \, \text{kV} = 20,000 \, \text{V}\).
Energy of electrons \(E = 20,000 \, \text{eV}\).
Using \( \lambda (\text{nm}) \approx \frac{1240}{V (\text{volts})} \):
Wait, the formula is \( \lambda \approx \frac{1240}{V} \text{ nm} \) if V is in Volts? No, \(E\) in eV.
\[ \lambda_{min} = \frac{1240}{20000} \, \text{nm} \]
\[ \lambda_{min} = \frac{124}{2000} \, \text{nm} = 0.062 \, \text{nm} \]
Alternatively in Angstroms:
\[ \lambda_{min} = \frac{12400}{20000} \, \text{\AA} = 0.62 \, \text{\AA} \]
Step 3: Check Options.
Option (A): 0.248 \AA
Option (B): 0.41 \AA
Option (C): 0.099 nm
Option (D): 0.062 nm (Matches our calculation)