Find the number of electron

Question: What is the maximum number of electron that can have principal quantum number n = 3 and spin quantum number; m = -1/2?

Solution: The principal quantum number represents the main shells to which the electron belongs. 

We can calculate the number of electron in each shell by the formula: 2n²

Where n represent number of shell.

Here principal quantum number i.e. n is 3.

Thus, number of electron in the shell is 2(3)²

                                                        = 18

So the maximum number of electron that have principal quantum number 3 is 18.

Spin quantum number accounts for spin of electron.  An electron can spin clockwise or anticlockwise, in two opposite directions. For clockwise spin value is +1/2 and for anticlockwise spin value is -1/2.  

Generally in each orbital half electron spin clockwise direction and half in anti-clockwise direction.

So the maximum number of electron that show spin quantum number -1/2 will be 9 in principal quantum number 3.