Chapter 6E: Quantum numbers

Schrodinger's Equation

Erwin Schrödinger developed an equation that incorporated wave and particle nature of electrons to describe their wave function over time

Quantum numbers

n - the principal quantum number

L- the orbital angular momentum quantum number

M(l)- angular momentum quantum number

M(s)- electron spin quantum number

Quantum Number Notation

(N, l, m1(l), m(s))

Principal Quantum number(n)

Relates energy and probable distance of the electron from the nucleus

• It describes the shell where the electron is located

• All electrons with the same value of n are in the same principal electron shell or level

• N can have a positive, non-zero, whole-number value

• N=1, 2,3,4…

Angular Momentum Quantum Number(l)

• It describes the shape of the orbital where the electron is located

• It describes the sub shell where the electron is located

• All electrons with the same value of n and l are in the same sub shell or sub level

• Can have a positive, whole-number value(including zero), but cannot be greater than n-1

• L= 0,1,2,n-1

Subshells

The number of subshells in a principal electronic shell is equal to the number of possible l values

• l=0=s

• L=1=p

• L=2=d

• L=3=f

• To designate a certain subshel within a principal electronic shell, we use the n value and the letter assigned to the subshell in question(called an orbital designation)

Magnetic Quantum Number(m(l))

m(l) describes the orientation of the orbital where the electron is located

• m(l) can have a negative or positive whole-number value(including zero), ranging from -1 too +1

m(l) = -1…-2,-1,0,1,2…+1

((2l+1)

Spin Quantum Number(m(s))

m(s) describes the orientation of the electron spin. Once you have m(s) specified, you are describing a single electron

• m(s) can have only two values, ½ and - ½

• this means there are two electrons per orbital or per m(l) value (2l+1)2