The Golden Ratio in X-ray Spectroscopy · AI Generator #GEN-2515E308

Physics · modern-physics

Problem

A materials scientist studying ancient artifacts discovers that a particular gold alloy produces characteristic X-rays with two prominent lines. The higher energy line has wavelength λ1=0.154  nm\lambda_1 = 0.154\;\text{nm} and the lower energy line has wavelength λ2=0.249  nm\lambda_2 = 0.249\;\text{nm}. Remarkably, the scientist finds that the ratio of these photon energies equals the famous golden ratio ϕ=1+52≈1.618\phi = \frac{1 + \sqrt{5}}{2} \approx 1.618. Verify this claim by calculating the actual ratio E1E2\frac{E_1}{E_2} of the photon energies.

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