# What is the maximum number of electrons allowed in #n = 2#?

##### 1 Answer

**THE MAIN QUANTUM NUMBERS OVERALL DEFINE AVAILABLE ORBITAL SUBSHELLS**

**principal quantum number**, indicating the *quantized* energy level, and corresponds to the period/row on the **periodic table**.

**angular momentum quantum number**, which corresponds to the *shape* of the orbital (

It defines a uniquesubshell.

With

Note that with

**THE MAGNETIC QUANTUM NUMBERS FURTHER DEFINE A SET OF (ORTHOGONAL) ORBITALS**

With **magnetic quantum number**

Therefore:

#\mathbf(m_l = 0)# for#l = 0# . For each#m_l# value, we have one orbital that corresponds.#\mathbf(m_l = -1, 0, +1)# for#l = 1# . For each#m_l# value, we have one orbital that corresponds.

Furthermore, we have the **spin quantum number** *cannot* be the same for two electrons with the same

That is, since all electrons in the same **orbital** have the same

That meanstwoelectrons per orbital only.

**TOTAL NUMBER OF ELECTRONS POSSIBLE**

Finally, with the

#(1 + 3) cancel("orbitals") xx "2 electrons"/cancel("orbital")#

#= color(blue)(8)# #color(blue)("electrons allowed")# which is what we expect for the

octet rulefor#n = 2# .