Hydrogen atom in its ground is excited by means of

Question

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.

Kevin Nash · Accepted Answer

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
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Modern Physics> Hydrogen atom in its ground is excited by...

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.

Radhika Batra , 11 Years ago

Kevin Nash

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Modern Physics> Hydrogen atom in its ground is excited by...

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.

Radhika Batra , 11 Years ago

Kevin Nash

LIVE ONLINE CLASSES

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