Chemistry Formula for Atomic Structure Part 2

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Chemistry Formulas for Atomic Structure

Chemistry Formulas from Bohr’s Model of Atom

·         Angular momentum of electron in nth orbit

 

Where, m = Mass of the electron,
            v = velocity of electron,
            r = radius of the orbit,
            h = Planck’s constant,
            n = no. of orbit in which electron is present,

·         Energy of electron in nth orbit

 
            
           Where, Z = Atomic No. of Electron,

·         Energy absorbed or released in an electron jump ( E)

 

·         Radius of orbits of hydrogen like species

 
              
         For hydrogen atom Z = 1, for first orbit n = 1,
         On substituting values of the constants
         h = 6.62×10-27erg sec,
         m = 9.1×10-28g,
         e = 4.8×10-10
     we get,
    r = 0.529 Å
So, radius of first orbit of hydrogen atom is 0.529 Å.

·         Radius of nth orbits of hydrogen like species

rn = 0.529n2/Z Å

·         Velocity of electron in nth orbit

 
          
      On substituting values of the constants
      We get,
 

·         No. of revolution per second made by an electron around the nucleus of atom

·         Energy of electron in nth orbit (En)

 
       
        On substituting values of the constants
        We get,          
            
         In general,
                          
 

·         Energy of electron in a Hydrogen Atom in different energy levels

Energy Level
E (Joules/atom)
E (eV/atom)
E (kcal/mol)
1
-21.79×10-19
-13.6
-313.5
2
-5.42×10-19
-3.4
-78.4
3
-2.41×10-19
-1.51
-38.84
4
-1.36×10-19
-0.85
-19.6
5
-0.87×10-19
-0.544
-12.5
Infinite
0
0
0
 

·         Frequency or wave length of emitted radiation

 
          
            Where, λ = wavelength of emitted radiations
                        R = Rydberg constant for Hydrogen atom

·         Number of spectral lines produced when an electron drops from nth level to ground level

 
          

 

Chemistry Formulas from Photoelectric Effect

·         Planck’s Relationship,

E = hv

·         Total energy,

Total Energy = (mv2/2) + w
Where, w = energy required to remove the electron.

Chemistry Formulas from Wave Mechanical Concept of Atom

·         De Broglie’s Equation,

 
            
          Where, m = mass of particle,
                        v = velocity of the particle,
                        h = Planck’s Constant,
or,       
          

Chemistry Formulas from Heisenberg’s Uncertainty Principle

·        Heisenberg’s Uncertainty Principle,

 
            
           Where,   = uncertainty in the position of the particle,
                        = uncertainty in the momentum of the particle,
Also,
           
 

Chemistry Formulas from Quantum Numbers

·         Principle Quantum Number (n),

Maximum no. of electrons in n principle quantum number = 2n2

·         Azimuthal Quantum Number (l),

For the given value of principle quantum number (n), azimuthal quantum number (l), may have all integral values from 0 to (n-1)

·         Magnetic Quantum Number (m),

No. of orbitals in a sub-shell = 2 l+1

·         Spin Quantum Number (s),

For spinning of electron about its own axis
 

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