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Question

A \( 30 \, \text{kV} \) X-ray tube produces X-rays. What is the minimum wavelength of the emitted
X-rays? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( c = 3 \times 10^8 \, \text{m/s} \), \( e
= 1.6 \times 10^{-19} \, \text{C} \))

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Explanation

**Photon energy** E = h f = h c/λ, momentum p = h/λ = E/c, power P = N E/t, N number of photons per second, wavelength λ = h c/E, for photon momentum 1.5×10⁻²⁷ kg·m/s frequency f = p c/h? Actually E = p c, f = E/h = p c/h =1.5×10⁻²⁷×3×10⁸/6.63×10⁻³⁴=6.79×10¹⁴ Hz, energy E= h f =4.5×10⁻¹⁹ J, for 5.0×10⁻¹⁹ J frequency f=E/h=7.54×10¹⁴ Hz. Energy E = e V = 1.6 × 10⁻¹⁹ × 30 × 10³ = 4.8 × 10⁻¹⁵ J . λₘiₙ = (h c/E) = (6.63 × 10⁻³⁴ × 3 × 10⁸/4.8 × 10⁻¹⁵) ≈ 4.14 × 10⁻¹¹ m =

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