Practice question

**X-rays from tube** maximum frequency f_max = e V/h, minimum wavelength λ_min = h c/(e V), Duane-Hunt law, for 10 kV f_max=1.6×10⁻¹⁹×10⁴/6.63×10⁻³⁴=2.41×10¹⁸ Hz, λ_min= c/f_max=0.124 nm, for 35 kV λ_min=1240/(35000) eV·nm? Actually 35 keV photon λ=1240/35000=0.0354 nm, for 15 kV 0.0827 nm, for 25 kV 0.0496 nm, for 30 kV 0.0413 nm. For a photon, p = (h v/c) , but also p = (h/λ) , and v = (c/λ) . So, v = (p c/h) , but directly, λ = (h/p) = (6.63 × 10⁻³⁴/1.5 × 10⁻²⁷) = 4.42 × 10⁻⁷ m . v = (c/λ) = (3 × 10⁸/4.42 × 10⁻⁷) ≈ 6.79