Atomic Structure - 7

Q.3. Wave function of 2s electron is given by . It has node at r = r₀. Find relation b/w r₀ & a₀.

Ans:
         ²₂₅ = 0 at r = r₀
[Dumb Question: Why ²₂₅ or prob. of finding electron is zero ?
  Ans: At r = r₀, it has node where probability of finding electron is zero.]

In this expression, only factor can be zero is
   2 - = 0   r₀ = 2a₀


Q.4. A dye absorbs light of = 4530 A⁰ & then fluorescence light of 50870 A⁰. 47% of absorbed energy is reemitted out as flurescence. Calculate ratio of quanta emitted out to no. of quanta absorbed.

Let n₁ photons areabsorbed.      _absorbed
Total energy absorbed =
E of light re-emitted out in one photon =
Let n₂ photons are reemitted then,
Total energy reemitted out =
As given
       E_absorbed x = E_{reemitted out}
       x = n₂ x
      
      


Dumb Question: What is fluorescence ?

Ans: Emission of radiation from particle ?


Q.5. Waht H-like ion has wavelength difference b/w I^st lines of Balmer & Lyman series equal to 59.3 nm   R_H = 109678 cm^-1

Ans: = R_Hz²
For I line of Balmer series
       = R_Hz² x R_H x z²
       _B =
       R_Hz
       _L =
       _B - _L = 59.3 x 10^-7 cm.
       = 59.3 x 10^-7
       [7.2 - 1.333] = 59.3 x 10^-7
       z² =
       z = 3
H-like atom is Li²⁺.