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IIT JEE Advanced 2008 Paper 1

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In a mixture of H and

He^{+}

gases (

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 collision). Assume that the Bohr model of atom is exactly valid.

Section: Physics

Question : 22 of 69

Marks: +1, -0

Solution:

As the electrons from the excited state (n = 4) falls to lower states, the energy is emitted. Therefore, for the transition n = 4→3, we have

13.6 ×

2^2\left(\frac{1}{9}-\frac{1}{16}\right)

\frac{hc}{\lambda e}

\frac{12,400}{\lambda \overset{0}{A}}

13.6 × 4 ×

\frac{7}{144}

\frac{12,400}{\lambda \overset{0}{A}}

⇒

\lambda \overset{0}{A}

\frac{12,400 \times 144}{13.6 \times 28}

= 4689

\overset{0}{A}

~ 4.8 ×

10^{-7}

The visible region is from

\lambda_1

= 4000

\overset{0}{A}

\lambda_2

= 7500

\overset{0}{A}

. For other transitions, λ lies outside the visible region.

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