Question:
A radiation of energy 11.0 eV is irradiated on gaseous hydrogen atoms at room temperature. Identify the energy level to which electron of hydrogen atom can be excited:
A radiation of energy 11.0 eV is irradiated on gaseous hydrogen atoms at room temperature. Identify the energy level to which electron of hydrogen atom can be excited:
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Hydrogen excitation depends on exact energy gaps between quantized levels.
Updated On: Jun 19, 2026
- \(E_5\)
- \(E_2\)
- \(E_3\)
- \(E_4\)
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The Correct Option is B
Solution and Explanation
Step 1: Use hydrogen energy level formula.
\[ E_n = -\frac{13.6}{n^2} \, eV \]
Step 2: Ground state energy.
\[ E_1 = -13.6\,eV \]
Step 3: Energy required for excitation.
From \(n=1\) to \(n=2\): \[ \Delta E = 13.6\left(1 - \frac{1}{4}\right) = 10.2\,eV \]
Step 4: Check given energy.
Given photon energy = 11.0 eV, which is enough to excite electron to \(n=2\) but not exactly higher stable levels.
Step 5: Higher level check.
To reach \(n=3\), required energy: \[ 12.09\,eV > 11.0\,eV \] So not possible.
Step 6: Final conclusion.
Thus, electron is excited to \(E_2\).
Final Answer: \[ \boxed{E_2} \]
\[ E_n = -\frac{13.6}{n^2} \, eV \]
Step 2: Ground state energy.
\[ E_1 = -13.6\,eV \]
Step 3: Energy required for excitation.
From \(n=1\) to \(n=2\): \[ \Delta E = 13.6\left(1 - \frac{1}{4}\right) = 10.2\,eV \]
Step 4: Check given energy.
Given photon energy = 11.0 eV, which is enough to excite electron to \(n=2\) but not exactly higher stable levels.
Step 5: Higher level check.
To reach \(n=3\), required energy: \[ 12.09\,eV > 11.0\,eV \] So not possible.
Step 6: Final conclusion.
Thus, electron is excited to \(E_2\).
Final Answer: \[ \boxed{E_2} \]
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