In a mixture of $\mathrm{H}-\mathrm{He}^{+}$gas ( $\mathrm{He}^{+}$is singly ionized He atom), H atoms and $\mathrm{He}^{+}$ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to $\mathrm{He}^{+}$ions (by collisions). Assume that the Bohr model of atom is exactly valid. The wavelength of light emitted in the visible region by $\mathrm{He}^{+}$ions after collisions with H atoms is

(C) $4.8 \times 10^{-7} \mathrm{~m}$

(A) $6.5 \times 10^{-7} \mathrm{~m}$

(B) $5.6 \times 10^{-7} \mathrm{~m}$

(D) $4.0 \times 10^{-7} \mathrm{~m}$

JEE Advanced · 2008 · 13 Apr 2008 · Paper 1 · Modern Physics

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

Answer: (C)

After the collision,

He^{+}

is in n=4 state. The visible transition is from n=4 to n=3. The energy difference is

Δ E = 13.6 \times 4 (\frac{1}{9} - \frac{1}{16}) = 54.4 \times \frac{7}{144} \approx 2.64

eV. Using

λ = \frac{h c}{E} = \frac{1240 eV\cdotnm}{2.64 eV} \approx 470

= 4.7 \times 1 0^{- 7}

m, which is closest to option (C).

JEE Advanced · 2008 · 13 Apr 2008 · Paper 1 · Single correct option