# Question 60897

Feb 2, 2017

The energies are almost equal, but slightly different, because the electrons in some orbitals spend more time closer to the nucleus.

#### Explanation:

In atoms of elements with more than one electron, each principal energy level is split into different sublevels.

For example, the order of increasing energy for orbitals in the fourth level is

$\text{4s < 4p < 4d < 4f}$

This is because the $\text{4s}$ orbitals have a greater electron density near the nucleus than the $\text{4p}$ orbitals, then come the $\text{4d}$ orbitals, and finally the $\text{4f}$ orbitals.

We can see this if we compare the "radial distribution functions" for each type of orbital, that is, the probability of finding an electron at a given distance from the nucleus.

We see that the $\text{4s}$ orbital (color(blue)("blue")color(white)(l) "line") has a local maximum quite close to the nucleus.
The $\text{4p}$ orbital ($\textcolor{p u r p \le}{\text{purple}}$) has its local maximum further out, and the "4d" color(white)(l)(color(olive)("olive"))# and $\text{4f}$ orbitals ($\textcolor{g r e e n}{\text{green}}$) have their local maxima still further from the nucleus.
Thus, a $\text{4s}$ electron spends more time close to the nucleus and has a lower energy level.
Next comes the $\text{4p}$, then the $\text{4d}$, and the furthest out $\text{4f}$ orbital has the highest energy of the group.