Question

The frequency of X-ray emitted by an X-ray tube operating at 30 kV is

• A. \(5.2 \times 10^{18} \, \text{Hz}\)
• B. \(6.2 \times 10^{18} \, \text{Hz}\)
• C. \(7.2 \times 10^{18} \, \text{Hz}\)
• D. \(2.2 \times 10^{18} \, \text{Hz}\)

Hint:

Planck’s equation E = hf relates energy and frequency in quantum mechanics. Always convert the X-ray energy from kV to joules before substituting into the formula. Accurate conversion ensures precise determination of X-ray frequencies, crucial for materials analysis and imaging applications.

Answer 1

The Correct Option is C

The frequency of the emitted X-ray is:
\[E = hf, \quad f = \frac{E}{h}\]
Given \(E = 30 \, \text{kV} = 30 \times 10^3 \times 1.602 \times 10^{-19} \, \text{J}\):
\[f = \frac{30 \times 10^3 \times 1.602 \times 10^{-19}}{6.626 \times 10^{-34}} \approx 7.2 \times 10^{18} \, \text{Hz}\]