Which one of the following statements about orbital energies is incorrect?
a) the energy of a given orbital increases as the nuclear charge z increases.
b) in many-electron atoms the energy of an orbital depends on both n and l.
c) inner electrons shield outer electrons more effectively than do electrons in the same orbital.
d) the splitting of sublevels in many-electron atoms is explained in terms of the penetration effect.
e) in the hydrogen atom, the energy of an orbital depends only on the value of the quantum number n.

A) The energy of a given orbital increases as the nuclear charge Z increases.

Explanation:

The energy of an orbital is as higher as the attraction force between protons and electrons is lower. So, as far as from nuclei, the orbital is more energetic. When Z increases, that means that the number of protons increases, so the attraction force increases, then the energy of a given orbital decrease.

Letter "b" is correct because of the Linus Pauling diagram in which the levels and sublevels are displaced to know its energy. The sublevel 3d is more energetic than the sublevel 4s, so it's necessary both quantum numbers.

Letter "c" is correct because the electrons at the same orbital have a greater repulsive force, so they can't shield electrons at the same orbital. But the inner electrons are attracted to the nuclei, so the repulsive force, plus the distance, will be less effective.

Letter "d" is correct because the penetration effect means the ability of an orbital to attract an electron. So, when the division in sublevels can explain that energy from the orbitals.

Letter "e" is correct because in the hydrogen atom there is only one orbital with one quantum number n and one quantum number l, which are n = 1, l = s, so the energy depends only on the quantum number n.

3 hours because it is a decent distance.