What is the value of n in the equation 1/2 (n – 4) – 3 = 3 – (2n + 3)?

n=2

Step-by-step explanation:

Step  1  :

           1

Simplify   —

           2

Equation at the end of step  1  :

   1                    

 ((— • (n - 4)) -  3) -  -2n  = 0

   2                    

Step  2  :

Equation at the end of step  2  :

  (n - 4)          

 (——————— -  3) -  -2n  = 0

     2            

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  2  as the denominator :

        3     3 • 2

   3 =  —  =  —————

        1       2  

8

Explanation:

1) Principal quantum number, n = 2

n is the principal quantum number and indicates the main energy level.

2) Second quantum number, ℓ

The second quantum number, ℓ,  is named, Azimuthal quantum number.

The possible values of ℓ are from 0 to n - 1.

Hence, since n = 2, there are two possible values for ℓ: 0, and 1.

This gives you two shapes for the orbitals: 0 corresponds to "s" orbitals, and 1 corresponds to "p" orbitals.

3) Third quantum number, mℓ

   The third quantum number, mℓ, is named magnetic quantum number.

The possible values for mℓ are from - ℓ to + ℓ.

Hence, the poosible values for mℓ when n = 2 are:

for ℓ = 0: mℓ = 0for ℓ = 1, mℓ = -1, 0, or +1.

4) Fourth quantum number, ms.

This is the spin number and it can be either +1/2  or -1/2.

Therfore the full set of possible states (different quantum number for a given atom) for n = 2 is:

(2, 0, 0 +1/2)(2, 0, 0, -1/2)(2, 1, - 1, + 1/2)(2, 1, -1, -1/2)(2, 1, 0, +1/2)(2, 1, 0, -1/2)(2, 1, 1, +1/2)(2, 1, 1, -1/2)

That is a total of 8 different possible states, which is the answer for the question.