IIT-JEE 2008 · Paper 1 · Physics Q42

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Passage

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 wavelength of light emitted in the visible region by He⁺ ions after collisions with H atoms is

6.5\times10^{-7}

5.6\times10^{-7}

4.8\times10^{-7}

4.0\times10^{-7}

Answer and worked solution

Official answer: C

Transitions from n = 4 in He⁺ ( $E_n=-54.4/n^2$ eV):

$4\to3$ : $54.4\left(\frac19-\frac1{16}\right)=2.64$ eV, $\lambda=\frac{1240}{2.64}\approx470$ nm: visible.
$4\to2$ (10.2 eV) and $4\to1$ (51 eV) are ultraviolet; $3\to2$ (7.6 eV) and others are UV too.

So the visible line is at about $4.7$ - $4.8\times10^{-7}$ m.

(C)

Topics:Bohr model and hydrogen spectrum

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IIT-JEE 2008 · Paper 1, Physics question 42