For a multielectron atom, a 3s orbital lies lower in energy than a 3p orbital because (LO 5.16) (a) a 3p orbital has more nodal surfaces than a 3s orbital. (b) an electron in a 3p orbital has a higher probability of being closer to the nucleus than an electron in a 3s orbital. (c) inner electrons shield electrons in a 3p orbital more effec-tively than electrons in a 3s orbital. (d) the energy of the electron can be spread between three 3p orbitals instead of only one 3s orbital.

Verified step by step guidance

1. First, let's understand the structure of an atom. The atom consists of a nucleus and electrons that move in orbitals around the nucleus. The energy of an electron in an orbital is determined by the principal quantum number (n), the angular momentum quantum number (l), and the magnetic quantum number (m).
2. The principal quantum number (n) determines the energy level or shell in which the electron is located. Both 3s and 3p orbitals are in the third energy level (n=3).
3. The angular momentum quantum number (l) determines the shape of the orbital. For an s orbital, l=0, and for a p orbital, l=1. The energy of an orbital increases with l within a given energy level. Therefore, a 3p orbital has higher energy than a 3s orbital.
4. The magnetic quantum number (m) determines the orientation of the orbital in space, but it does not affect the energy of the orbital.
5. Finally, the shielding effect refers to the ability of inner electrons to shield outer electrons from the positive charge of the nucleus. The shielding effect is more significant for s orbitals than for p orbitals because s electrons are closer to the nucleus and are more effective at shielding. Therefore, the shielding effect lowers the energy of a 3s orbital compared to a 3p orbital.

Key Concepts

Orbital Energy Levels

In multielectron atoms, the energy levels of orbitals are influenced by their shape and the distribution of electrons. Generally, s orbitals are lower in energy than p orbitals within the same principal energy level due to their spherical shape, which allows electrons to be closer to the nucleus and experience less shielding from inner electrons.

Shielding Effect

The shielding effect occurs when inner electrons partially block the attractive force of the nucleus on outer electrons. In a multielectron atom, electrons in p orbitals are more shielded by inner electrons compared to those in s orbitals, leading to higher energy levels for p orbitals due to reduced effective nuclear charge experienced by the outer electrons.

Nodal Surfaces

Nodal surfaces are regions in an orbital where the probability of finding an electron is zero. The presence of nodal surfaces affects the energy of orbitals; for instance, p orbitals have one nodal plane, while s orbitals have none. This difference contributes to the higher energy of p orbitals compared to s orbitals, as more nodal surfaces generally indicate higher energy states.