Quatum Number

Is a number which describe the characteristics of electrons.
It's used to characterize electrons as they occupy orbitals in different energy levels.
It also describe the main energy level, orientation of orbitals and spinning of electrons.

Four types of quantum numbers

1.Principle quantum number (n) .
Is the number that specifies the location and the energy of electron.
This number (n) describes the main energy level of electrons. The principle quantum number is also called the shell orbit, the main energy level or the stationary state.
The principle quantum numbers have specific names from the nucleus. Denoted by K, L, M, N etc.

2. Subsidiary principle quantum number (l) .
Is a number specifying shapes of orbitals in a shell.
Subsidiary principle quantum number is a sub energy level.
This sub energy level is known as azimuthal quantum number, sub shell or sub energy level. The shell is divided to form sub shells.
The total number of sub shells in each shell is simply equal to the number of shells from the nucleus.
The known sub shells are s, p, d, f, g, h and i. The values of sub energy levels is in the order of 0, 1, 2, …L = n - 1.

The value of L must be smaller that n.
As l is given by n – 1.

3. Magnetic quantum number (ml).
Is the one that specifies the number of orbitals present in a given value of subsidiary quantum number.
This describes the orientation of orbitals in a shell .
When the sub shell divides form orbitals, it's these orbitals that are called magnetic quantum number.
1s – Orbital s = O(spherical in nature)

3p – Orbital =p

4. Spin quantum number (s).
This is a quantum number that describes the direction in which the electrons spin.
As there are two maximum number of electrons moving in opposite directions.
One revolving in a clockwise (+ ½) while the other in an anti – clock wise (– ½) manners.

Application of Quantum Number.

To find;
i. The number of sub shells (l),
ii. Number of orbitals (m) and
iii. The total number of electrons (s) of the given quantum number (n).

Determination of total number of sub shells, orbitals and electrons in an atom.
Two methods are recommended.

Example #01.
(a) Find the total number of electrons in the principle quantum number 2.

Solution.
Method #01,tree diagram

Total subshells, 2 =s & p
Orbitals, 4 = 0,-1,0,+1
Electrons, 8

Method # 02;
By using tabular form.

(b) Find the total number of electrons in the principle quantum number 3 .(use a tabular form)

Solution.

Total subshells = 3
Orbitals, 9= 0,-1,0,+1,-2,-1,0,+1,+2.
Electrons= 18.

So
Problem # 08.
(a) The modern theory of electron behaviour is based on two assumptions. State them
Answer.

(b) Define the following terms
i. Orbital.
ii. Energy levels of atoms.
iii A shell.

iv. Quantum.
Answer

Problem # 09.
Write short notes on the following statements:
(a) Quantization of energy and radiation.
Answer
(b) Wave particles duality of matter.
Answer
(c) Quantum number.
Answer

Problem # 10
(a) Distinguish between the following terms:-
(i) An orbital and orbit.
(ii) S – Orbital and P – orbital.
(iii) A quantum of light and quantization of energy.
(iv) Quantum shell and quantum number.
Answer

(b) Explain briefly the meaning of the following quantum numbers:-
(i) n
(ii) l
(iii) m
(iv) ms
Answer

(c) In a tabular form specify all the four quantum numbers for each electron in an atom whose n value is 2. Given that all the orbitals are full of electrons.
Answer

(d) Given the value of the quantum numbers n, l and m for the electron with the highest energy in sodium atom in the ground state.
Answer

(e) Write down all quantum numbers of all the electrons in the ground state of nitrogen
atom.
Answer

(f) Give the values of all the four quantum numbers for 2p electrons in Nitrogen.
Answer

(g) Briefly explain why the following quantum numbers are not allowed?.
i) n = 1, l = 1, m = 0
ii) n = 1, l = 0, m = 2
iii) n = 4, l = 3, m = 4
iv) n = 0, l = -1, m = 1
v) n = 2, l = -1, m = 1.
Answer

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