In Moseley's Law, σ (sigma) represents the screening constant. It accounts for the shielding effect of inner-shell electrons on the effective nuclear charge experienced by an electron undergoing transition that results in X-ray emission.
Explanation of the Screening Constant
Moseley's Law describes the relationship between the frequency (or wavelength) of characteristic X-rays emitted by an element and its atomic number (Z). The law is expressed as:
√ν = C(Z - σ)
Where:
- ν is the frequency of the emitted X-ray.
- C is a constant proportional to the Rydberg constant (R).
- Z is the atomic number of the element.
- σ is the screening constant.
The screening constant (σ) arises because the electrons closer to the nucleus partially shield the outer electrons from the full positive charge of the nucleus. Instead of experiencing a nuclear charge of +Z, the outer electrons experience an effective nuclear charge (Zeff) which is less than Z. The screening constant provides an approximation of how much the inner electrons are reducing the effect of the total charge. Thus:
Zeff = Z - σ
Significance of the Screening Constant
- Correction for Electron Shielding: The screening constant corrects for the fact that the electrons involved in X-ray emission don't "feel" the full nuclear charge due to the presence of other electrons.
- Approximation: It's an approximation because the exact shielding effect is complex and depends on the electron configuration of the atom. The value of σ is typically around 1 for K-alpha transitions.
- Improved Accuracy: Incorporating the screening constant into Moseley's Law improves the accuracy of predicting X-ray frequencies, especially for elements with larger atomic numbers.
