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← IIT-JEE 2008 · Paper 1
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IIT-JEE 2008 · Paper 1, Physics question 41

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Paragraph for Question Nos. 41 to 43

In a mixture of H-He⁺ gas (He⁺ is singly ionized He atom), H atoms and He⁺ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He⁺ ions (by collisions). Assume that the Bohr model of atom is exactly valid.

The quantum number nn of the state finally populated in He⁺ ions is

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Answer and worked solution

Official answer: C

Energy given by H. Its excitation energy in the first excited state is 13.6(1−14)=10.213.6\left(1-\frac14\right)=10.2 eV.

He⁺ in n = 2. E2=−54.44=−13.6E_2=-\dfrac{54.4}4=-13.6 eV. Adding 10.2 eV gives −3.4-3.4 eV.

New level. −54.4n2=−3.4-\dfrac{54.4}{n^2}=-3.4 gives n2=16n^2=16, n=4n=4.

(C)

Topics:Bohr model and hydrogen spectrum
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