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.
Hund's Rule.
Aufbau's Principle.