Question

An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be :

• A. $10^{-1}$ nm
• B. $10^{-2}$ nm
• C. $10^{-3}$ nm
• D. $10^{-4}$ nm

Hint:

$1 \text{ nm} = 10 \text{ \AA}$. Always double-check the units (nm vs \AA) when using the shortcut constant 12400 or 1242.

Answer 1

The Correct Option is C

Step 1: Use the formula $\lambda_{min} (\text{in \AA}) = \frac{12400}{V (\text{in Volts})}$.
Step 2: Given $V = 1.24 \times 10^6\ \text{V}$.
Step 3: $\lambda_{min} = \frac{12400}{1.24 \times 10^6} = \frac{1.24 \times 10^4}{1.24 \times 10^6} = 10^{-2}\ \text{\AA}$.
Step 4: Convert \AA\ to nm: $10^{-2}\ \text{\AA} = 10^{-2} \times 10^{-1}\ \text{nm} = 10^{-3}\ \text{nm}$.