Sigma (σ) in Zeff represents the screening constant. In the context of effective nuclear charge (Zeff), it quantifies the reduction in the full nuclear charge (Z) experienced by an electron due to the shielding effect of other electrons in an atom. The reference states: Zeff=Z−σ.
Understanding Zeff and Sigma
To fully grasp the meaning of sigma, let's break down the concept of effective nuclear charge (Zeff):
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Zeff (Effective Nuclear Charge): This is the net positive charge experienced by an electron in a multi-electron atom. Because of the presence of other electrons, the outer electrons are shielded from the full nuclear charge.
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Z (Atomic Number): This represents the total number of protons in the nucleus of an atom, which also equals the full nuclear charge.
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σ (Screening Constant): Also known as the shielding constant, it represents the extent to which other electrons shield a particular electron from the full nuclear charge. A higher value of sigma indicates greater shielding.
How Sigma Works:
The inner electrons "screen" or "shield" the outer electrons from the full positive charge of the nucleus. Because of this shielding effect, the outer electrons experience a reduced positive charge. The screening constant (σ) estimates the amount of this reduction.
Example
Consider an electron in a polyelectronic atom. If the full nuclear charge (Z) is 10, but the electron experiences an effective nuclear charge (Zeff) of 6, then the screening constant (σ) would be 4.
Zeff = Z - σ
6 = 10 - σ
σ = 4
Factors Affecting Sigma
The value of sigma (screening constant) is influenced by several factors, including:
- Number of inner electrons: More inner electrons generally lead to a larger screening constant.
- Electron Configuration: Electrons in inner shells shield outer electrons more effectively than electrons in the same shell.
