Chemistry Formulas for Atomic Structure

Chemistry Formulas from Bohr’s Model of Atom

·         Angular momentum of electron in n^th 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 n^th 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 = 6.62x10^-27erg sec,

         m = 9.1x10^-28g,

         e = 4.8x10^-10

     we get,

    r = 0.529 Å

So, radius of first orbit of hydrogen atom is 0.529 Å.

·         Radius of n^th orbits of hydrogen like species

r_n = 0.529n²/Z Å

·         Velocity of electron in n^th 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 n^th orbit (E_n)

       
        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	-21.79x10-19	-13.6	-313.5
2	-5.42x10-19	-3.4	-78.4
3	-2.41x10-19	-1.51	-38.84
4	-1.36x10-19	-0.85	-19.6
5	-0.87x10-19	-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 n^th 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

Chemistry Formulas for Structure of Atom Part 1