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Question

Find the wavelength of the radiation required to excite the electron in Li++ from the first to the third Bohr orbit. You may need to use the constant hc = 1242 eV.nm.

A
13.6 nm
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B
11.4 nm
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C
27.2 nm
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D
6.8 nm
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Solution

The correct option is B 11.4 nm
So I have to give sufficient energy to excite an electron from the 1st orbit of Li++ ion to 3rd. So what is the energy of Li++ ion in the ground state.
E1=13.6Z2n2.
Z = 3, n = 1

E1 = 9 × (-13.6) eV.
Similarly if I give it sufficient energy and the electron reaches 3rd orbit then the energy of the ion will be

E2=13.6Z2n2.
Z = 3, n = 3

E2=13.6eV.

So the energy that would be required to achieve it should be.
E2E1=8×(13.6)=108.8eV.

Now the wavelength of this light of energy 108.8 eV could be found by .....
I know hcλ.
Simple

hcλ = 108.8

λ = 11.4 nm

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