Question

An X-ray tube operates at 30 kV. If one electron converts 10% of its energy into a photon at first collision, then the wavelength of the photon (correct to two decimal places) is ........ A. [h = $4.14 \times 10^{-15}$ eV·s, c = $3 \times 10^{8}$ m/s] 
 

Hint:

For X-ray calculations, use $\lambda(\text{\AA}) = \frac{12400}{E(\text{eV})}$ as a shortcut.

Answer 1

Correct Answer: 4.1

Step 1: Calculate electron energy.
Voltage = 30 kV = \(30{,}000\) eV. 10% of this energy produces the photon: \[ E = 0.10 \times 30{,}000 = 3000\ \text{eV} \] Step 2: Use the photon energy formula.
\[ E = \frac{hc}{\lambda} \] \[ \lambda = \frac{hc}{E} \] Step 3: Substitute values.
\[ \lambda = \frac{(4.14 \times 10^{-15})(3 \times 10^{8})}{3000} \] Convert to Å (1 Å = \(10^{-10}\) m): \[ \lambda = \frac{1.242 \times 10^{-6}}{3000} = 4.14 \times 10^{-10}\ \text{m} \] \[ \lambda = 4.14\ \text{\AA} \] Step 4: Conclusion.
Wavelength of the photon = 4.14 Å.