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The ionization energy of a hydrogen like Bohr atoms is 4 Rydbergs. (i) What is the wavelength of the radiation emitted when the electrons jumps from the first excited state to the ground state ? (ii) What is the radius of the first orbit for this atom ?

The ionization energy of a hydrogen like Bohr atoms is 4 Rydbergs. (i) What is the wavelength of the radiation emitted when the electrons jumps from the first excited state to the ground state ? (ii) What is the radius of the first orbit for this atom ? 

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
7 years ago
Hello Student,
Please find the answer to your question
(i) En = - I.E. / n2 for Bohr’s hydrogen atom.
Here, I.E. = 4R ∴ En = -4R / n2
∴ E2 – E1 = -4R / 22 – (- 4R / l2) = 3 R …(i)
E2 - E1 = hv = hc /λ ….(iii)
From (i) and (ii)
hc / λ = 3R
∴ λ = hc / 3R = 6.6 x 10-34 x 3 x 108 / 2.2 x 10-18 x 3 = 300Å
(ii) The radius of the first orbit
Bohr’s radius of hydrogen atom = 5 x 10-11 m (given)
|En| = + 0.22 x 10-17 Z2 = 4 R = 4 x 2.2 x 10-18
∴ Z = 2
∴ rn­ = r0 / Z = 5 x 10-11 / Z = 5 x 10-11 / 2 = 2.5 x 10-11 m
Thanks
Kevin Nash
askIITians Faculty

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