ATOMIC STRUCTURE

1. Planck's Quantum Theory
   E = hν = 
   hcλ
   
   where h = Planck's Constant (6.023 x 10^-34 Js) , ν = Frequency of radiation , c = Velocity of Light , λ = Wavelength of radiation
   c = νλ and wave number = 
   1λ
2. Moseley's Equation
   √ν = a (z - b)
3. Heisenberg's uncertainity Equation
   Δp . Δx ≥ 
   h4π
    and ΔE . Δt ≥ 
   h4π
   
   Kinetic Energy of electron in the nth quantum state = 
   12
    
   Zke²r_n
   
   Potential Energy of electron in the nth quantum state = - 
   Zke²r_n
   
   Total energy (E) = - 
   Zke²2r_n
    = - 
   (13.6)Z²n²
   eV per atom
                = - 
   313.6n²
    kcal / mol = - 
   1312n²
    kJ / mol
                = - 21.8 x 10^-19
   Z²n²
    J / atom
4. Radius of nth quantum state = 
   n²h²4π²mkZe²
    = 
   n²a_oZ
   (a_o = 0.529 A)
5. Velocity of electron (v_n) = 
   2ρZke²nh
    = 
   Zn
    x 2.188 x 10⁶ m/s
   No. of revolutions per second in r.p.s. = 
   v_n2πr_n
    = 
   Zv_n2πn²a_o
   
   Wave number of spectral line ,
   
6. de Broglie Equation 
   Azimuthal (or angular) Quantum number (l) ; 0 ≤ l ≤ n - 1
   Orbital angular momentum , L = √l ( l + 1 )
   h2π
   
   Magnetic quantum number (m); - l ≤ m ≤ l , total (2l + 1)
   Magnetic Moment , μ_L = 
   eh4πmc
   √l ( l + 1 )
   Spin angular momentum = √s( s + 1 )
   h2π
7. Aufbau Principle 
   Subshell qith lowest (n + l) , value is filled first , if two subshells have same (n + l) value , lower value of 'n' is filled up first .
8. Photoelectric Effect 
   Maximum kinectic energy of ejected electron
   
   12
    mv²_max = hν - hν_o
   Stopping Potential , eV = hν - hν_o
   
   Binding Energy = Mass Effect x 931 MeV
   
   
   • Radius of Nucleus (r_n) = r_o x A^1/3 , where A is the mass number and r_o is proportionality constant whose value is 1.4 x 10^-13 cm
   • Although energy of electron increases with the increase in the value of n (orbit) , yet the difference of energy between successive orbits decreases .
     Thus , E₂ - E₁ > E₃ - E₂ > E₄ - E₃ > E₅ - E₄....etc.
   • No. of spectral lines when electron comes from n^th level to ground level = n (n + 1)/2
   • No. of sub-shells in a main energy level = n
   • No. of orbitals in a main energy level = n²
   • No .of orbitals in a sub shell = (2l+1)
   • No. of electron in each orbit = 2
   • Maximum no. of electron in a sub shell = 2 (2l+1)
   • Maximum no. of electron in a main shell = 2n²