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Hydrogen atom in its ground is excited by means of monochromatic radiation of wavelength 975 Å. How many different lines are possible in the resulting spectrum ? Calculate the longest wavelength amongst them. You may assume the ionization energy for hydrogen atom as 13.6 eV.

Hydrogen atom in its ground is excited by means of monochromatic radiation of wavelength 975 Å. How many different lines are possible in the resulting spectrum ? Calculate the longest wavelength amongst them. You may assume the ionization energy for hydrogen atom as 13.6 eV.

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
8 years ago
Hello Student,
Please find the answer to your question
E = 12400 / λ (in Å) eV = 12400 / 975 = 12.75 eV … (i)
Also
13.6 [ 1 / n21 – 1 / n22] = 12. 75 ⇒ [1 /1 – 1 / n22] = 12.75 / 13. 6 ⇒ n2 = 4
For every possible transition one downward arrow is shown therefore the possibilities are 6.
Note : For longest wavelength, the frequency should be smallest.
This corresponds to the transition from n = 4 to n = 3, the energy will be E4 = 13.6 / 42 ; E3 = - 13.6 / 32
∴ E4 – E3 = 13.6 / 42 – (- 13.6 / 32) = 13.6 [1/9 – 1/16]
= 0.66 eV = 0.66 x 1.6 x 10-19 J = 1.056 x 10-19 J
Now, E = 12400 / λ (inÅ) eV ∴ λ = 18787 Å
Thanks
Kevin Nash
askIITians Faculty

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