Atomic Structure - 8

Q.1. 1.8g H - atoms are excited to radiation. Spectra shows that 27% of atoms are in III^rd energy level & 1.5% of atoms in II^nd energy level & rest in ground state. Ionization potential of H is 13.6 ev. Calculate
(i) No. of atoms present in III, II energy level.
(ii) Total energy envolved when all atoms return to ground state.

Ans: 1g H contains = No atoms
       1.8g H contains = 6.023 x 10²³ x 1.8
                              = 10.84 x 10²³ atoms

(a) No. of atoms in III shell =
                                           = 292.68 x 10²¹ atoms.
                                           = = 162.6 x 10²¹ atoms.

(b) When all atoms return ti I shell, then
     E' = (E₃ - E₁) x 292.68 x 10²¹
     E_n = - ev
     E' = (- + 13.6) x 292.68 x 10²¹ x 1.6 x 10^-19     [ 1 ev = 1.6 x 10^-19 J]
        = 5.668 x 10⁵ J
     E'' = (E₂ - E₁) x 162.6 x 10²¹
         = (- + 13.6) x 1.6 x 10^-19 x 162.6 x 10²¹
         = 2.657 x 10⁵ J
     E = E' + E'' = (5.668 + 2.657) x 10⁵ J
     Total energy envolved = 832.5 KJ


Q.2. Find quantum no. 'n' corresponding to excited state of He⁺ ion if on transitiontoground state that ion emits two photons in succession with wavelengths 18.5 & 30.4 nm respectively.

Ans: Suppose electron in excited state is present in n₂ shell. First it falls from n₂ to n₁ & then from n₁ to ground state (n = 1).
(i) n₂ n_{1      1} = 108.5 nm
(ii) n₁ G.State,      ₂ = 30.4 nm
     
      = 1 - 0.75   n₁² =
     n₁ = 2

Again,
     
                  = 109677 x 2²
      = 0.25 - 0.21 = 0.04
     n₂² = = 25   n₂ = 5


Q.3. The wave function of orbital is given by (r) = . Find thevalue of r for which probability of finding electron is max.

Ans: Probability of finding electron
       ²(r) =
For max. probability finding electron
         &  
       ..................
       = e^-c[(-4ar)e^-2br + e^-2br(-2b)]
               = e^-ce^-2br[- 4ar - 2b]
                  [- 4ar - 2b] = 0
                  4ar = - 2b
                
       = (- a) + (- 4ar - 2b)²
              = [- 4a + (4ar + 2b)²]
              =[- 4a + 16a²r² + 4b² + 16abr]
Putting   r = -
              =[- 4a + 16a² x + 4b² + 16ab x -]
              = [- 4a + ]
        
Max. prob. of finding electron
when   r = -


Key Words

Bohr's Model of atom.
Photoelectric effect.
Emission Spectra.
Absorption Spectra.
Rydberg's Formula.
De broglie Wavelength.
Heisen berg's Uncertainity Principle.
Wave Function
Quantum No. &
     Principal Quantum No.
     Azimuthal Quantum No.
     Amgnetic Quantum No.
     Spin Quantum No.
Paulieexclusion Principle.
Nodal Plane.
Nund's Law.
Aufbaw's Principle