# Penetration and Shielding

Electrons are negatively charged and are pretty close to each other, which means that they can repel each other. The repulsion an electron feels is shielding and the attraction it feels to the nucleus is penetration. The specific math is Coulomb's Law (an analogy with classical physics): F=kqQ/r2. The force that an electron feels is dependent on the distance from the nearest charge (i.e., an electron, usually with bigger atoms and on the outer shells) and the amount of charge. More distance between the charges will result in less force, and more charge will have more force of attraction.

### Introduction

In an ideal setting (for atoms at least), every electron should feel the same amount of "pull" from the nucleus. This means that the negative to positive charge ratio should be 1:1.

However, that is not the case when observing atomic behavior. When considering the core electrons (or the electrons closest to the nucleus), the ratio is 1:1, or at least close to it. As you proceed from the core electrons to the outer valence rings of electrons, the negative to positive charge ratio falls below 1:1. This is because of shielding, or simply the electrons repelling each other, but these same core electrons penetrate and feel more of the nucleus than the other electrons.

### Shielding

To wit: An atom (assuming its atomic number is greater than 2) has core electrons that are extremely attracted to the nucleus in the middle of the atom. However the number of protons in the nucleus are never equal to the number of core electrons (relatively) adjacent to the nucleus. The number of protons increase by one across the periodic table, but the number of core electons change by periods.  The first period has no core electrons, the second has 2, the third has 10, and etc. This number is not equal to the number of protons. So that means that the core electrons feel a stronger pull towards the nucleus than any other electron within the system. The valence electrons are farther out from the nucleus, so they experience a smaller force of attraction.

Shielding refers to the core electrons repelling the outer rings and thus lowering the 1:1 ratio. The nucleus has "less grip" on the outer electrons and are shielded from them.

### Penetration

However, contrary to what many think, penetration is not the outer electrons penetrating through the shield of the core electrons. It is actually just how well the electrons feel the nucleus. This is SIMILIAR to the idea of outer electrons penetrating, but not the same. They are not the same because the core electrons have more penetration than the outer electrons since they (the core electrons) feel the strongest pull.

To relate the idea of penetration, we can use the idea of $$Z_{eff}$$ or the effective nuclear charge. It is essentially the number of protons' charge minus the number of electrons shielding- basically how effective the nucleus is at attracting the electrons. Since core electrons do not shield themselves, they penetrate the most and are exposed to the most (effective) nuclear charge.

### References

1. R. S. Mulliken, Electronic Structures of Molecules and Valence. II General Considerations, Physical Review, vol. 41, pp. 49-71 (1932)
2. Anastopoulos, Charis (2008). Particle Or Wave: The Evolution of the Concept of Matter in Modern Physics. Princeton University Press. pp. 236–237. ISBN 0691135126.

### Problems

1. Which electrons shields better in an atom? 2s or 2p? 3p or 3d?
2. Why can we relate classical physics to quantum mechanics when it comes to subatomic activity?
3. What is penetration?

1. 2s shields the atom better than 2p because the s orbitals is much closer and surrounds the nucleus more than the p orbitals, which extend farther out.  3p shields better than 3d, because p orbitals are closer to the nucleus than the 3d orbitals.
2. Classical physics and quantum mechanics both can deal with subatomic activity such as electron interactions, orbital location, size, and shape, and distances to find forces of attractions.
3. Penetration is how well the outer electrons are shielded from the nucleus by the core electrons.  The outer electrons therefore experience less of an attraction to the nucleus.

### Contributors

• Alan Chu

19:58, 30 Nov 2013

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