Quantum

The state of an electron in an atom is given by four quantum number.

1.      Principal Quantum Number (n)

            To represent the position of an electron of an atom in the shells or energy level of the atom.

The following are the n values and the shell numbers of an atom.

            K         L          M         N         O         P          Q

            1          2          3          4          5          6          7

2.      Angular Momentum Quantum Number (l)

            To show the position of an electron in a sub shell or sub energy level. Sub shells are parts of a shell in an atom.

The value range of l, start from : 0,1,……..(n – 1)

In which n = principal quantum number.

Sub shell are represented with lower case letters.

s if l = 0

p if l = 1

d if l = 2

f if l = 4

Note:

Orbital is a space that can be occupied by up to (maximally) 2 electrons. Every sub shell has a different number of orbital. Therefore, every sub shell also has a different nimber of electrons.

The name of an orbital is determined by n value and l value.

For example:

Orbital 3s : number 3 indicates the third shell (M), and s indicates the sub shell (l = 0).

           

3.      Magnetic Quantum Number (m_l)

            To represent the spatial orientation of an electron in an arbital (or the position of an electron in an orbital).

The value of m_l start from – l up to +l

The following is a table showing the value of l, m_l, and the number of orbital in sub shells.

l	Sub Shells	ml	Number of Orbital
0	s	0	1
1	p	-1,0,+1	3
2	d	-2,-1,0,1,2	5
3	f	-3,-2,-1,0,+1,+2,+3	7

4.      Spin Quantum Number (m_s)

            To show the direction of an electron’s rotation (spin) in an orbital. Each electron spins (rotates) to an opposite direction to each other.

There are two m_s values, namely: + ½  (up) and – ½ (down).

EXERCISE

1.  Give the labels of all of the groups of orbitals if n = 3, and state how many m_l values are there in each group!

Answer:

The quntum number : l, from 0 up to (n – 1)

N = 3, l = 0,1,2.

The labels for the groups of the orbitals are then: 3s, 3p, 3d.

The quntum number: m_l: from – l up to + l

So the number of m_l values is 2l + 1

This gives:         one 3s orbital

                        three 3p orbitals

                        five 3d orbitals