7. Electronic configuration of the Element..

According to Rutherford model of an atom, atom is made of outer electron cloud   (-vely charged electron) and inner nucleus (neutral neutron and +vely charged proton).Niels Bohr agreed with this concept , he also agreed that electron revolve round the nucleus like a planet moves round sun.He applied the Plank's quantum theory to the electron revolving round the nucleus
         The orbits , there fore called as energy levels or energy shells. Bohr gave numbers 1, 2, 3, ...etc to these energy levels, there are they now called as Principal quantum numbers.these energy levels are also designated by  k, l, m, n, etc...

The energy levels which are more far from the nucleus associated with greater amount of energy                                                        -The energy of outermost electron is greater than innermost.

-These outermost electron helps atom to react with other because they can pullout easily  from the orbital .

-Each shell made of many sub shells which are themselves composed of atomic orbitals.

-First shell K  have 1 sub shell = s

-Second shell L  = 2 sub shells = s , p

-Third shell M = 3 sub shells =s , p, d

-fourth shell N = 4 sub shells = s , p, ,d, f

No.	Sub shell	Name
1	s	Sharp
2	p	Principal
3	D	Diffused
4	f	fundamental

Shells	Sub shells	No. of electron	Type of sub shells found in shell	Distribution electron in sub shells
K	s	2	only s	1s
L	P	6	s ,p,	2s , 2p,
M	d	10	s, p, d,	3s , 3p, ,3d
N	f	14	s, p, ,d, f , d,	4s , 4p , 4d , 4f
…	g and so on	18…	s , p, d, f, g,…	Alphabetically  so on

-The reactivity of the element is highly dependent upon its electronic configuration.

- The distribution of electron in various orbital (s, p,d ,f ) is known as electronic configuration.

-Mathematically it is described by Slater rules.

-In representing position of electron in various shells and sub shells ,the following rules are observed..

=> Major  energy shells written first then sub shells and after that the no. of electron in particular sub shell

for example :-     

1s²,   where ,   1 represents the shell i.e. K

                        s represent the sub shell
                    and  2 indicates the no of electron present in sub shell.

-According to Afbau principal--

               The electrons enter in the various orbitals in the order of increasing energy.

- According to pauli exclusion principal--

                An orbital can contain a maximum of 2 electron and these two electrons must be in opposite spin.                                              

                                                                       

↑

↓

                                                            

-According to Hund's rule--

           It states that electron pairing in orbital of the same energy level will not take place unless all available orbitals of subshell contain one electron  each with parallel spin.   

Order of filling of electron in various orbitals is given below :--

Above picture shows normal periodic table of element, but from the picture given below we can find the outermost orbital of the element and electronic configuration.

There are some special cases of electronic configuration.
From periodic table we can see that the electronic configuration of the elements  are going in normal way till Argon(18) last electron goes in 3p orbital. But in case of Potassium(19) last electron should fill in 3d orbital but it is not so, it goes in 4s orbital instead of 3d orbital because 4s has low energy in comparison to 3d .Thus electron prefer to go in lower energy orbital then higher energy level.

-The next ten elements from ( Z=21 to 30) Sc to Zn are called Transition elements.
In these elements addition of electron take place in inner 3d orbitals while outer 4s orbital remains fully occupied.



6. Plank's quantum theory and Radiant energy

Radiant energy-

       It is a most powerful natural source of energy.It travel in the form of wave .It can be visible or non visible some time ...It  is used in the field of Radiometry, solar energy, heating , lighting ..etc. and also in the field of telecommunication.

Concept of radiant energy -
 -According to j.c. Maxwell (1864), alternating currents of high frequency is capable of radiating energy in the form of waves.
-These waves travel in space with the same speed as light,these waves are called as electromagnetic waves or electromagnetic radiations.

 -This  electromagnetic radiation is a form of energy which propagate through the space in the form of waves which are associated with electric and magnetic field.
- Velocity of radiation  
                              C = λv,
            Where v is frequency, and λ is wave length of the radiation.

All type of  electromagnetic radiation travel with the same velocity but they differ in their frequency and wavelength.


Plank's Quantum Theory of Radiation- Theory to explain spectral distribution of radiant energy

According to Plank's Quantum theory..

1. Radiant energy is not emitted or absorb continuously but discontinuously in the form

of small bundles of energy  called as Quanta.

2. The  quantum of light is called photon (i.e.  mass less bundle of energy )

3.Each quantum is associated with a definite amount of energy E  which is proportional
to the frequency of radiation  
                            
                               E = hv

where h= plank's constant and (h=6.62688x10⁻²⁷ erg sec or 6.626x10⁻ᶟ⁴J s.)

A body can absorb or emit energy in whole number multiples of quantum, i.e.  E=nhv
   where n = 1, 2, 3, ....

This means body can absorb or emit  energy equal to 1 hv, 2 hv, 3 hv...etc. Energy in fraction can't  be absorbed or lost.

     This is called quantisation of energy.

5. Bohr's theory of an atom..

According to Rutherford model of an atom, atom is made of outer electron cloud   (-vely charged electron) and inner nucleus (neutral neutron and +vely charged proton).Niels Bohr agreed with this concept , he also agreed that electron revolve round the nucleus like a planet moves round sun. But when he applied the Plank's quantum theory to the electron revolving round the nucleus , he found some important facts that are disscused below.

Postulates of Bohr's theory--

 1-      An electron revolves around the nucleus in an orbit (like planet revolve around the sun) with a constant energy.  During this motion electron neither loses nor gains energy.

    In othert word the energy of an electron remains constant in a perticular orbit, it means each orbit is associoated with a definite energy i.e. with a definite  whole number of quanta of energy.
         The orbits , there fore called as energy levels or energy shells. Bohr gave numbers 1, 2, 3, ...etc to these energy levels, there are they now called as Principal quantum numbers.these energy levels are also designted by  k, l, m, n, etc...

The energy levels which are more far from the nucleus associated with greater amount of energy.

2-   Energy is emmited or absorbed by an atom only when an electron moves from one orbit(energy level) to another.

3-  The angular momentum of an electron  moving round the nucleus is quantised.
   Angular momentum = mvr =   n ( h/2π )
( where n is any integer number( 1, 2, 3, ...etc ) and m is mass, v is linear velocity of electron , while r is the radius of the orbit.)

Thus the angular momentum of any electron may be h/2π  or a whole number multiple of h/2π , 2h/2π  , 3h/2π....nh/2π . This is called  quantisation of angular momentum. 

Bohr' equation--
 Bohr was able  to calculate energy of electron moving in different orbits round the nucleus in Hydrogen atom.
       Electron contineus to remain in its orbit because  the electrostatic force of attraction exerted by nucleus is balanced by the centrifugal force arising from its circular motion.

 if the charge on the  hydrogen atom nucleus = +Ze.
     For hydrogen Z = 1 and hydrogen like atom such as He⁺ and Li⁺⁺ ,
 Z= 2 and 3 respectively.

The electron with charge  -e revolves round the nucleus in an orbit of radius r,with the tangential velocity v . If mass of electron is m

Then ,
     
    Electrostatic force acting on electron by the nucleus   =   (Ze )x e/r² = Ze²/r²

centrifugal force acting on electron  arising by circular motion = mv²/r

Both the forces balance to the electron during its motion thus,  
                                      mv²/r        =      Ze²/r²         --------(1)
                                                          
                                                                v²=Ze² / mr           --------(2
according to bohr's postulate , angular momentum  = mvr  =    n ( h/2π )  
                          
                                                  v = nh/2πmr             --------(3)

This equation  is called velocity of n electron.

   then                       v²     =   n²h²/4π ²m²r                          --------(4)
                              
                                   Ze²/mr  =  n²h²/4π ²m²r²                ----------(5)                     

                                   Ze²  = n²h²/4 π²mr                              ----------(6)

hence radius  of nth orbit is =    rn     =     n²h²/4 π²m Ze² 
  
for H atom Z = 1 then    ,
                                                                rn     =     n²h²/4 π²m e²         ----------(7)

for   H atom  n = 1 in ground state , the   radius r is designated as Bohr's radius (aₒ)

                                     a ₒ      =       h²/4 π²m e²            ----------(8)

The total energy of the revolving electron = k.energy =1/2mv²)+pot. Energy (-Ze²/r)
                   E = 1/2mv² + (-Ze²/r)    ----------(9)

                E = 1/2mv² - Ze²/r           ----------(10)
                 thus ,
                        1/2mv² =   Ze²/r     ----------(11)
substituting the value of mv²  in above equation
   E  =      Ze²/2r  - Ze²/r        =  -Ze²/2r      ----------(12)

After substituting the value of r  =     n²h²/4 π²m Ze²  we get  ,

                                                E  =      -Ze²/2  x  4 π²m Ze²/n²h²     ---------(13)  
 Thus the energy of electron in nth orbital is ........

                                                En =  2π²m Z²e⁴ / n²h²      ----------(14)

This  equation is Bohr equation . this equation is applicable to hydrogen and hydrogen like atoms  such as He+ , Li++ , Be+++, etc.