In which energy level would the f orbital make their first apperance? ( use quantum mechanical proof your answer)
Please help, I don't get what's the question asking! Thank you
The orbitals, in order, are
1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f etc.
However, this is not the order if which they fill since the energy levels don't follow sequentially as in the listing above. For example, 1s fills first, 2s next, 2p next, 3s, then 3p, then 4s followed by 3d. The question is asking which n (1,2,3,4,5, etc) level the f orbital fills first AND to prove it by quantum mechanics.
Is it going to be n= 4 right ? Because 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f <- s this the quantum mechanics?
I don't think so. Ce (#58) is the first element to have an f electron and Ce is in period 6. And no, that is not a quantum mechanical answer or proof.
http://www.webelements.com/cerium/atoms.html
The question is asking about the energy level at which the f orbital would first appear in an atom. To answer this question using quantum mechanics, we need to understand the concept of electron energy levels and the order in which orbitals are filled.
In quantum mechanics, electrons are described by their wave-like properties and are located in specific energy levels around the nucleus of an atom. These energy levels are often referred to as "shells" or "principal quantum numbers" (n).
Each energy level can be further divided into sublevels, which are denoted by the letters s, p, d, and f. These sublevels represent different shapes and orientations of the electron orbitals.
The Aufbau principle states that electrons fill the lowest energy levels first before occupying higher energy levels. Additionally, the order of filling the sublevels is as follows: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, etc.
From this order, we can determine that the f orbital would first appear in the 4th energy level, specifically in the 4f sublevel. The 4f sublevel follows the filling of the 4s and 3d sublevels.
Therefore, the answer is that the f orbital makes its first appearance in the 4th energy level (n = 4).
To recap, we used the rules of quantum mechanics, specifically the Aufbau principle, to determine the energy level at which the f orbital would first appear.