# How to determine the number of electron in a shell [duplicate]

My textbook has been mentioned that the maximum number of electron in a shell is 2n² and the octet rule. It has also said that period number signifies the number of electron shells of an element and group number signifies number of valence electrons in a shell. When I tried to distribute electrons on basis of above mentioned laws,it was not true for all elements. For eg. Rubidium-37 the electron is distributed as 2,8,18,8,1 here, there are 5 shells and valence electron 1 which satisfies the statement about period and group number but when I tried to do the same with Caesium-55 this is what it's electrons distribution look like 2,8,18,8,8,8,3 which neglects the statement given in my book. Please tell what has gone wrong here. Please explain in simple words as I am a high school student.

• Does your textbook mention Aufbau's rule? Aug 15 '20 at 4:50
• Caesium is in the sixth period. How many shells does it have? Aug 15 '20 at 5:44
• @Peter Do you know about s, p, d and f orbitals and blocks. Because if you do it will be easier to explain. Aug 15 '20 at 14:22
• @Habib "Aufbau" is not a person. It is a term derived from the German word for building up. So it is Aufbau rule rather than Aufbau's rule. Aug 31 '20 at 0:25

I'll try to keep it simple. The actual details of why this is so has to do with quantum physics.

Each shell has several "subshells". Each "subshell" in turn holds a certain number of "orbitals". Each orbital can hold up two electrons. Rules of thumb (again, I'm not explaining why because it's probably way out of your understanding)

1. The $$\mathrm {n^{th}}$$ shell has n subshells, labelled from $$0$$ to $$\mathrm n-1$$. E.g., the $$2$$nd shell has two subshells, $$0$$ and $$1$$. For reference, we often call these subshells by letters, $$0$$ is $$\mathrm s$$, $$1$$ is p, $$2$$ is d and $$3$$ is f. The periodic table can be broken up into four blocks depending on which of these subshells the most loosely bound (valence) electron in the atom is in. (s-block, p-block, etc)

2. The $$\mathrm{k^{th}}$$ subshell can hold $$2\mathrm k+1$$ "orbitals". An orbital can hold up to two electrons. So, the $$0$$th (s) subshell can hold $$1$$ orbital, and thus two electrons. The $$1$$st subshell (p) can hold $$3$$ orbitals, or $$6$$ electrons. This is why we have the $$2\mathrm n^2$$ rule. There are as many orbitals in the $$\mathrm n$$ shell as the sum of the first mathrm n odd numbers: $$\mathrm n^2$$, and two electrons in each ($$2\mathrm n^2$$).

3. An important idea in physical chemistry is the Aufbau principle. Orbitals are filled according to the increasing order of their (orbitals') energies. What are the orbitals' energies? It's quite simple for the first few subshells:

$$1\mathrm s, 2\mathrm s, 2\mathrm p, 3\mathrm s, 3\mathrm p$$ (order)

In a hydrogen atom, these orbitals are straightforward: all subshells in the same shell have identical energies ($$1 \mathrm s, 2\mathrm s=2\mathrm p, 3\mathrm s=3\mathrm p=3\mathrm d,$$ etc). In other atoms, though, everything gets tangled up. Here is the order, something you will need to memorise:

$$1\mathrm s, 2\mathrm s, 2\mathrm p, 3\mathrm s, 3\mathrm p, 4\mathrm s, 3\mathrm d, 4\mathrm p, 5\mathrm s, 4\mathrm d, 5\mathrm p, 6\mathrm s, 4\mathrm f, 5\mathrm d, 6\mathrm p, 7\mathrm s, [...]$$ (this will do for most elements, but there are some exceptions, which you will have to memorise as well)

So the electrons don't actually fill the entire $$2\mathrm n^2$$ in a shell before going to the next. E.g., in iron, we have the configuration $$1\mathrm s^2 2\mathrm s^2 2\mathrm p^6 3\mathrm s^2 3\mathrm p^6 4\mathrm s^2 3\mathrm d^6$$. Note that the $$1$$ shell has $$2$$ electrons; the $$2^{\mathrm {nd}}$$ shell, $$8 (2\mathrm s+2\mathrm p$$); the $$3^{\mathrm{rd}}$$ shell, $$14 (3\mathrm s+3\mathrm p+3\mathrm d)$$; the $$4^{\mathrm {th}}$$ shell, $$2$$. Your textbook might call this configuration (2, 8, 14, 2)\$.

Caesium has 55 electrons, they fill up like so: $$1\mathrm s^2 2\mathrm s^2 2\mathrm p^6 3\mathrm s^2 3\mathrm p^6 4\mathrm s^2 3\mathrm d^{10} 4\mathrm p^6 5\mathrm s^2 4\mathrm d^{10} 5\mathrm p^6 6\mathrm s^1$$.

Why don't you add the number of electrons in each shell up and see if it matches what your textbook says.

P.S. The octet rule doesn't actually say the highest shell should have eight electrons. It says that the atom achieves stability by gaining the electronic configuration of the nearest noble gas. Noble gases have the general configuration $$\mathrm s^2 \mathrm p^6$$ ($$8$$ electrons?), but as demonstrated above, these $$8$$ electrons may not be in the highest shell. For example, in iron, two of the valence electrons are in the fourth shell and the other six in the third shell.