The ionization energy of a hydrogen like Bohr atom

Question

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 ?

Kevin Nash · Accepted Answer

Hello Student,

Please find the answer to your question

(i) E_n = - I.E. / n² for Bohr’s hydrogen atom.

Here, I.E. = 4R ∴ E_n = -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)

|E_n| = + 0.22 x 10^-17 Z² = 4 R = 4 x 2.2 x 10^-18

∴ Z = 2

∴ r_n = r₀ / Z = 5 x 10^-11 / Z = 5 x 10^-11 / 2 = 2.5 x 10^-11 m

Thanks
Kevin Nash
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Modern Physics> The ionization energy of a hydrogen like ...

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 ?

Radhika Batra , 11 Years ago

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LIVE ONLINE CLASSES

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