QUANTUM NUMBERS at a glance

 

Rules guiding the arrangement of electrons in an atom

When electrons are arranged or filled into the atoms of elements, certain RULES are considered   and obeyed. These rules are the Aufbau's Principle, Pauli's exclusion principle and Hund’s rule of maximum multiplicity.

PAULI EXCLUSION PRINCIPLE 

states that NO two electrons in the same atom have the sets of the four quantum numbers {n, l, m and s in an atom}.

AUFBAU PRINCIPLE states that "when electrons go into atoms they fill orbitals of lower energy first before filling orbitals of higher energy and each orbital may hold up to two electrons.

 

HUND’S RULE OF MAXIMUM MULTIPLICITY state that " When electrons fill degenerate orbitals they go in singly first before pairing up occurs.

 Degenerate Orbitals are orbitals that are at the same energy level. example of degenerate orbitals is the P-orbital, the d-orbital or the f-orbital

Examples of degenerate orbitals are the P-orbitals,  the d-orbitals  and the f-orbitals 

QUANTUM NUMBERS

The quantum numbers are a set of numbers that describes the position of an electron in an atom. 

Studies have showed  that the energy of an electron may be characterized by four quantum numbers. These quantum numbers help to locate the position of electrons in an atom

1. The principal quantum number represented by n with integral values of 1,2,3,4 e.t.c.

This quantum number describes the shell ( k, l, m....)

2. The subsidiary or Azimuthal quantum number represented by l with integral values ranging from 0 to (n-1).

This quantum number describes the sub-shells ( s,p,d,f,)

3.  The magnetic quantum number represented by m with integral values ranging from –l ,0, +l.

4. The spin quantum number represented by s with integral values – ¹/₂ and + ¹/₂.

Element   At. Numb.  Elect. Conf.

 H .            1;             1s¹

He              2;         1s²

Li.               3;         1s² 2s¹

Be              4;          1s² 2s²

B =.           5;          1s² 2s² 2p¹

C =            6;          1s² 2s² 2p²

N =.          7 ;         1s²2s²2p3      

O=            8 ;       1s² 2s² 2p⁴

F=.           9;         1s² 2s² 2p⁵

Ne=        10;         1s² 2s² 2p⁶

Na=.         11;        1s² 2s² 2p⁶ 3s¹

Mg=          12;     1s² 2s² 2p⁶ 3s²

Al=.        13;   1s² 2s² 2p⁶ 3s² 3p¹

Si =       14;    1s² 2s² 2p⁶ 3s² 3p²

P=.       15;     1s² 2s² 2p⁶3s²³3p³

S =.       16;   1s² 2² 2p⁶3s² 3p⁴

Cl =.    17;     1s² 2s² 2p⁶ 3s² 3p⁵

Ar =.   18      1s² 2s² 2p⁶ 3s²3p⁶

K=.    19  1s² 2s² 2p⁶ 3s²3p⁶ 4s¹

Ca =.  20  1s² 2s² 2p⁶ 3s²3p⁶ 4s²

OBJECTIV QUESTION

1.  Which of the following orbitals is spherical in shape?

     (a) s

      (b) p

      (c) d 

      (d) f

  

2.     Which of the following shells have a maximum of eight electrons?

             (a)  K

             (b) L 

             (c) M 

             (d) N

3.     1s² 2s² 2p⁶ 3p¹ is the electronic configuration of

              (a)  potassium

               (b) calcium 

               (c) sodium

              (d) aluminum.

4  . “Two electrons in an atom cannot have the same set for all four quantum numbers”. This statement is

              (a)  Aufbau principle 

               (b) Pauli exclusion 

               (c) Hund’s rule

              (d) Rutherford’s model.

5.    Which of the quantum number is represented by L?

              (a)  principal quantum number

              (b) subsidiary quantum number                  

              (c) magnetic quantum number

              (d) spin quantum.

6.    Pauli exclusion principles related 

a). quantity of electrons in the valence shell

b). filling the orbitals with lower energy first 

c). the filling of degenerate orbitals 

d). quantum numbers of electrons.

7. Atomic orbital is 

a). the circular path through which electrons which electrons revolve round the nucleus 

b). a region around the nucleus where electrons are most likely to be found 

c). the path around the nucleus through which electrons move 

d). the path around the nucleus through which protons move.

THEORY QUESTIONS 

  1(a)(i)what are the quantum numbers 

   (ii). The models below represent the filling of orbitals in an atom

   

State which rule(s) is/are violated or obeyed by each model

(iii).     State the following principle (a) Pauli exclusion principle. (b) Aufbau principle

(b). Write the electronic configuration of 

(i) Oxygen   (ii) Calcium (iii) Fluoride ion (Cl^-) (iv) Potassium ion  (K⁺)    (v). Aluminum ion (Al³⁺

2.a(i). List the quantum numbers that are assigned to an electron in an atom.

(ii) what is the maximum number of electrons that can occupy the 3d orbital?

3.(a)State 

I.  Pauli's exclusion principle 

ii. Hund's rule of maximum multiplicity

iii. Write the electronic configuration of of each of the following ions of copper I. Cu+ 

II. Cu2+.       [29Cu]