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A double ionized Lithium atom is hydrogen-like with atomic number 3. (i) Find the wavelength of the radiation required to excite the electron in Li ++ form the first to the third Bohr orbit. (Ionization energy of the hydrogen atom equals 13.6 eV.) (ii) How many spectral lines are observed in the emission spectrum of the above excited system ?

A double ionized Lithium atom is hydrogen-like with atomic number 3. 
(i) Find the wavelength of the radiation required to excite the electron in Li++ form the first to the third Bohr orbit. (Ionization energy of the hydrogen atom equals 13.6 eV.)
(ii) How many spectral lines are observed in the emission spectrum of the above excited system ?

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
9 years ago
Hello Student,
Please find the answer to your question
. (i) En = - 13.6 / n2 Z2 eV / atom
For Li2+ , Z = 3 ∴ En = - 13.6 x 9 / n2 eV / atom
∴ E1 = - 13. 6 x 9 / 1 and E3 = - 13.6 x 9 / 9 = - 13. 6
∆E = E3 – E1 = - 13. 6 – (- 13.6 x 9)
13. 6 x 8 = 108.8 eV /atom
Λ = 12400 / E (in eV) Å = 12400 / 108.8 = 114 Å
(ii) The spectral line observed will be three namely 3 ⟶ 1,
3⟶ 2, ⟶ 1.
Thanks
Kevin Nash
askIITians Faculty

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