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Paragraph: In a mixture of H - H ⁺ gas ( He ⁺ . is singly ionised He atom), H atoms and He ⁺ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He ⁺ ions (by collisions). Assume that the Bohr model of atom is exactly valid. Question: The wavelength of light emitted in the visible region by He ⁺ ions after collisions with H atoms is

Options

  1. A6.5 10⁻⁷ ~m
  2. B5.6 10⁻⁷ ~m
  3. C4.8 10⁻⁷ ~m
  4. D4.0 10⁻⁷ ~m

Correct answer

C. 4.8 10⁻⁷ ~m

Step-by-step solution

Visible light lies in the range, ₁=4000 Å to ₂=7000 Å . Energy of photons corresponding to these wavelengths (in eV ) would be; aligned & E₁= 12375 4000 =3.09 eV & E₂= 12375 7000 =1.77 eV aligned From energy level diagram of He ⁺ atom we can see that in transition from n=4 to n=3 , energy of photon released will lie between E₁ and E₂ . E₄₃=-3.4-(-6.04)=2.64 eV Wavelength of photon corresponding to this energy. = 12375 2.64 Å=4687.5 Å=4.68 10⁻⁷ ~m Therefore, (c) is the most correct option.

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