what is the effect of electrons in a penetrating orbital on Z* (the effective nuclear charge) felt by electrons in a second orbital?
The penetrating electron decreases the effective nuclear charge (increases the shielding) BUT not equal to 1 electron (because it just penetrates and doesn't stay in one place).
Not sure what you are asking but ... electrons in inner shells reduce the attraction between the (positive) nucleus and outer electron shells.
To understand the effect of electrons in a penetrating orbital on the effective nuclear charge (Z*) felt by electrons in a second orbital, we need to consider the concept of shielding or screening effect.
The electron-electron repulsion plays a crucial role in determining the effective nuclear charge experienced by an electron in an atom. Electrons in the inner shells (closer to the nucleus) tend to effectively screen or shield the outer electrons from the positive charge of the nucleus. This shielding effect reduces the attractive force between the nucleus and the outer electrons.
When we talk about penetrating orbitals, we refer to orbitals that have a higher probability of being closer to the nucleus, meaning they have higher penetration into the regions occupied by the inner electrons. Orbitals with lower principal quantum numbers (n) have higher penetration than those with higher values of n. For example, a 2s orbital is more penetrating than a 2p orbital.
Now, when an electron in a penetrating orbital approaches the nucleus, it partially cancels out the shielding effect of the inner electrons. This is because the electron in the penetrating orbital has a higher probability of being found closer to the nucleus, thus reducing the repulsion between the inner electrons and the outer electron in the second orbital. As a result, the effective nuclear charge (Z*) experienced by the electron in the second orbital increases.
Therefore, the presence of electrons in penetrating orbitals enhances the effective nuclear charge (Z*) felt by electrons in a second orbital due to reduced electron-electron repulsion.
In summary, electrons in penetrating orbitals reduce the shielding effect of inner electrons, leading to an increase in the effective nuclear charge (Z*) experienced by electrons in a second orbital.