Is this always true, sometime true, or never true?
The orbitals of a principal energy level are lower in energy than the orbitals in the next higher principal energy level.
-I'm thinking sometime true but I can't figure out how to explain why it sometime true. Thanks
I think you're right. It is true sometimes but not all the time.
The best way I think is to show examples.
12Mg = 1s2 2s2 2p6 3s2
Here the 1s orbital is lower than the 2s and they are lower than the 3s etc.
19K = 1s2 2s2 2p6 3s2 3p6 3d0 4s2
Here the 1s is lower than the 2s and those are lower than the 3s and the 4s BUT the 4s level is lower than the 3d.
The statement is always true. The orbitals of a principal energy level are indeed lower in energy than the orbitals in the next higher principal energy level. This principle is known as the Aufbau principle, which states that electrons fill the lowest energy level available before moving on to higher energy levels. As you move further away from the nucleus, the energy levels increase, and therefore, the orbitals of higher principal energy levels have higher energy than the orbitals in the lower principal energy level.
You're correct, the statement is sometimes true. Let me explain why and how you can figure it out.
The energy levels in an atom are composed of sublevels, which are further composed of orbitals. Each principal energy level has multiple sublevels, and each sublevel has multiple orbitals. The energy of the orbitals within a principal energy level is determined by their distance from the nucleus, with orbitals closer to the nucleus having lower energy.
Now, let's consider the two scenarios mentioned in the statement:
1. Lower in energy: In some cases, the orbitals within a principal energy level can indeed have lower energy than the orbitals in the next higher principal energy level. This occurs when the sublevel of the higher energy level has higher angular momentum (i.e., higher value of l). For example, the 2p orbital in the second principal energy level has higher energy than the 2s orbital in the same energy level.
2. Higher in energy: However, there are also cases where the orbitals in a higher principal energy level have lower energy than the orbitals in the lower energy level. This happens when the higher energy level has fewer nodes in its electron density distribution, making it closer to the nucleus and thus lower in energy. This occurs when the sublevel of the lower energy level has higher angular momentum (i.e., higher value of l). For instance, the 3d orbital in the third principal energy level has lower energy than the 4s orbital in the fourth principal energy level.
To determine whether the statement is true for a specific case, you need to compare the sublevels and their respective orbitals in the energy levels you're considering. By understanding the relationship between the principal energy levels, sublevels, and orbitals, you can determine whether the orbitals of a principal energy level are lower or higher in energy than those in the next higher principal energy level.