Part of JPH-02 — Atoms: Bohr Model & Hydrogen Spectrum

X-rays and Moseley's Law

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X-rays are produced when high-energy electrons strike a metal target. The continuous spectrum (bremsstrahlung) has a minimum wavelength lambdaminlambda_{min} = hceV\frac{hc}{eV} = 12400/V Angstrom, determined only by the accelerating voltage V, independent of target material. The characteristic spectrum consists of sharp lines (K-alpha, K-beta, L-alpha, etc.) that depend on the target element. Moseley's law: sqrt(f) = a(Z - b), where a and b are constants. For K-series, b approximately equals 1 (one remaining K electron screens the nucleus). For L-series, b approximately equals 7.4. This connects to Bohr's model: K-alpha X-rays correspond to an L-shell electron filling a K-shell vacancy, equivalent to a 2 to 1 transition with effective nuclear charge (Z-1). So 1/lambda = R*(Z-1)^2*(1/1^2 - 1/2^2) = 3R(Z-1)^2/4. Moseley's law proved that atomic number Z, not atomic mass, is the fundamental property ordering elements.

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