JEE Advanced · Physics · 27. Atomic Physics
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In a mixture of \(\mathrm{H}-\mathrm{H}^{+}\)gas \(\left(\mathrm{He}^{+}\right.\)is singly ionised \(\mathrm{He}\) atom), \(\mathrm{H}\) atoms and \(\mathrm{He}^{+}\)ions are excited to their respective first excited states. Subsequently, \(\mathrm{H}\) atoms transfer their total excitation energy to \(\mathrm{He}^{+}\)ions (by collisions). Assume that the Bohr model of atom is exactly valid.
Question:
The wavelength of light emitted in the visible region by \(\mathrm{He}^{+}\)ions after collisions with \(\mathrm{H}\) atoms is
- A \(6.5 \times 10^{-7} \mathrm{~m}\)
- B \(5.6 \times 10^{-7} \mathrm{~m}\)
- C \(4.8 \times 10^{-7} \mathrm{~m}\)
- D \(4.0 \times 10^{-7} \mathrm{~m}\)
Answer & Solution
Correct Answer
(C) \(4.8 \times 10^{-7} \mathrm{~m}\)
Step-by-step Solution
Detailed explanation
Visible light lies in the range, \(\lambda_1=4000 Å\) to \(\lambda_2=7000 Å\).
Energy of photons corresponding to these wavelengths (in \(\mathrm{eV}\) ) would be;
\(
\begin{aligned}
& E_1=\frac{12375}{4000}=3.09 \mathrm{eV} \\
& E_2=\frac{12375}{7000}=1.77 \mathrm{eV}
\end{aligned}
\)
From energy level diagram of \(\mathrm{He}^{+}\)atom we can see that in transition from \(n=4\) to \(n=3\), energy of photon released will lie between \(E_1\) and \(E_2\).
\(
\Delta E_{43}=-3.4-(-6.04)=2.64 \mathrm{eV}
\)
Wavelength of photon corresponding to this energy.
\(
\lambda=\frac{12375}{2.64} Å=4687.5 Å=4.68 \times 10^{-7} \mathrm{~m}
\)
Therefore, (c) is the most correct option.
Energy of photons corresponding to these wavelengths (in \(\mathrm{eV}\) ) would be;
\(
\begin{aligned}
& E_1=\frac{12375}{4000}=3.09 \mathrm{eV} \\
& E_2=\frac{12375}{7000}=1.77 \mathrm{eV}
\end{aligned}
\)
From energy level diagram of \(\mathrm{He}^{+}\)atom we can see that in transition from \(n=4\) to \(n=3\), energy of photon released will lie between \(E_1\) and \(E_2\).
\(
\Delta E_{43}=-3.4-(-6.04)=2.64 \mathrm{eV}
\)
Wavelength of photon corresponding to this energy.
\(
\lambda=\frac{12375}{2.64} Å=4687.5 Å=4.68 \times 10^{-7} \mathrm{~m}
\)
Therefore, (c) is the most correct option.
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