💡 X-rays
Cut-off (minimum) wavelength λ_min = hc/(eV) = 12400/V Å (V in volts). Moseley's law: √ν = a (Z − b) for characteristic X-ray frequency ν. Kα line energy (approx): E = 13.6 (Z−1)² (1/1² − 1/2²) eV = 10.2 (Z−1)² eV (screening constant b ≈ 1).
X-ray calculators
Cut-off λ_min, Moseley frequency, Kα energy
Accelerating voltage (V)
Cut-off wavelength
248 Å
Atomic number (Z)
Z (e.g. Cu=29)
Screening constant (b)
b ≈ 1 for K
Constant a (×10⁷ √Hz)
a × 10⁷
√ν (√Hz) & frequency ν (Hz)
—
Atomic number (Z)
Z ≥ 2
Kα line energy
8046 eV
📡 X-ray summary
Run a calculation to see result.
🧮Step-by-Step Solution▼ Show
| Concept | Formula | Notes |
|---|---|---|
| Cut-off / minimum wavelength | λ_min = hc/(eV) = 12400/V (Å) | V = accelerating voltage in volts |
| Moseley's law | √ν = a (Z − b) | ν = frequency of characteristic X-rays |
| Energy of Kα line (approx) | E = 13.6 (Z−1)² (1/1² − 1/2²) eV | Screening constant b ≈ 1; E = 10.2 (Z−1)² eV |
About X-rays
When electrons are accelerated through a voltage V and strike a target, the shortest (cut-off) X-ray wavelength is λ_min = hc/(eV) = 12400/V Å (V in volts). Characteristic X-rays follow Moseley's law √ν = a (Z − b); for the K series b ≈ 1. The Kα line (transition n=2 → n=1) has approximate energy E = 13.6 (Z−1)² (1/1² − 1/2²) eV = 10.2 (Z−1)² eV.