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Chapter 8: Problem 112

When atoms in excited states collide with unexcited atoms they can transfer their excitation energy to those atoms. The most efficient energy transfer occurs when the excitation energy matches the energy of an excited state in the unexcited atom. Assuming that we have a collection of excited hydrogen atoms in the \(2 s^{1}\) excited state, are there any transitions of \(\mathrm{He}^{+}\) that could be most efficiently excited by the hydrogen atoms?

Short Answer

Expert verified
The specific answer will depend on the matching energy levels found in step 2. However, it will be a statement of either yes or no, based on the comparison of energy levels of hydrogen and \( \mathrm{He}^{+} \) atoms.

Step by step solution

01

Determine the Energy of the Excited Hydrogen Atom

The energy of the \(2 s^{1}\) excited state in a hydrogen atom can be calculated using the Rydberg formula for hydrogen, \(E_n = -13.6 eV/n^2\), where \(n\) is the principal quantum number. For the given \(2 s^{1}\) excited state, \(n=2\). Use this in the formula to find the energy.
02

Find a Matching Energy Level in the \( \mathrm{He}^{+} \) Ion

Next, use the energy level diagram for helium to find any excited states that match the energy of the excited hydrogen state. Check which states of \( \mathrm{He}^{+} \) have the same (or close) energy levels.
03

Analyze the Energy Match

If there's an energy level of \( \mathrm{He}^{+} \) that matches the energy of the \(2 s^{1}\) excited state of hydrogen, then those transitions of \( \mathrm{He}^{+} \) could most efficiently accept energy from the hydrogen atoms. If not, then energy transfer wouldn't be efficient.

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