Question:
The energy required (in eV) to excite an electron of H-atom from the ground state to the third state is
The energy required (in eV) to excite an electron of H-atom from the ground state to the third state is
Show Hint
For hydrogen atom,
\[
E_n=\frac{-13.6}{n^2}\,\text{eV}
\]
Excitation energy is always calculated using
\[
\Delta E=E_f-E_i
\]
where \(E_f\) is the final energy level and \(E_i\) is the initial energy level.
Updated On: Jun 22, 2026
- \(+0.85\)
- \(-3.4\)
- \(12.1\)
- \(-12.1\)
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Use the energy formula for hydrogen atom.
The energy of the \(n^{\text{th}}\) orbit in hydrogen atom is given by \[ E_n=\frac{-13.6}{n^2}\,\text{eV} \]
Step 2: Find the energy of the ground state.
For the ground state, \[ n=1 \] Therefore, \[ E_1=\frac{-13.6}{1^2} \] \[ E_1=-13.6\,\text{eV} \]
Step 3: Find the energy of the third state.
The third state corresponds to \[ n=3 \] Thus, \[ E_3=\frac{-13.6}{3^2} \] \[ E_3=\frac{-13.6}{9} \] \[ E_3=-1.51\,\text{eV} \]
Step 4: Calculate the excitation energy.
Energy required to excite the electron from ground state to third state is \[ \Delta E=E_3-E_1 \] \[ \Delta E=(-1.51)-(-13.6) \] \[ \Delta E=12.09\,\text{eV} \] \[ \Delta E\approx 12.1\,\text{eV} \]
Step 5: Final conclusion.
Therefore, the required excitation energy is \[ \boxed{12.1\,\text{eV}} \]
The energy of the \(n^{\text{th}}\) orbit in hydrogen atom is given by \[ E_n=\frac{-13.6}{n^2}\,\text{eV} \]
Step 2: Find the energy of the ground state.
For the ground state, \[ n=1 \] Therefore, \[ E_1=\frac{-13.6}{1^2} \] \[ E_1=-13.6\,\text{eV} \]
Step 3: Find the energy of the third state.
The third state corresponds to \[ n=3 \] Thus, \[ E_3=\frac{-13.6}{3^2} \] \[ E_3=\frac{-13.6}{9} \] \[ E_3=-1.51\,\text{eV} \]
Step 4: Calculate the excitation energy.
Energy required to excite the electron from ground state to third state is \[ \Delta E=E_3-E_1 \] \[ \Delta E=(-1.51)-(-13.6) \] \[ \Delta E=12.09\,\text{eV} \] \[ \Delta E\approx 12.1\,\text{eV} \]
Step 5: Final conclusion.
Therefore, the required excitation energy is \[ \boxed{12.1\,\text{eV}} \]
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