Q14. The ground state energy of an electron in a hydrogen atom is –13.60 eV.
The energy of the electron in the third excited state is _________eV
(rounded off to two decimal places).
The energy of the electron in the third excited state of a hydrogen atom is -0.85 eV. This value comes from the Bohr model energy formula applied to the principal quantum number n=4 for the third excited state.
Energy Formula
The total energy En of an electron in the nth energy level of a hydrogen atom follows En = -13.60/n2 eV, where the ground state (n=1) gives -13.60 eV. Higher levels have less negative (higher) energies, approaching zero as n increases.
Identify State
Ground state is n=1. First excited state is n=2, second is n=3, and third excited state is n=4. No options appear in the query, but common distractors include errors like using n=3 (-3.06 eV) or forgetting the negative sign (+0.85 eV).
Calculation Steps
For n=4: E4 = -13.60/16 = -0.85 eV. This matches standard references and rounds to two decimal places as required.
SEO Optimized Content
In the Bohr model of the hydrogen atom, understanding energy levels is crucial for competitive exams like CSIR NET Life Sciences, JEE, and NEET, where questions test the hydrogen atom third excited state energy from the ground state value of -13.60 eV. The quantized energy formula En = -13.60n2 eV directly yields the third excited state energy as -0.85 eV, essential for spectral line calculations and atomic physics.
Bohr Model Basics
Niels Bohr’s model treats the electron in circular orbits around the proton, with energy inversely proportional to n squared. Ground state (n=1) binds the electron tightly at -13.60 eV; excitation raises n, reducing binding energy.
Step-by-Step Solution
- Confirm third excited state: n=4 (sequence: n=1 ground, n=2 first, n=3 second, n=4 third).
- Apply formula: E4 = -13.60/42 = -13.60/16 = -0.85 eV.
- Verification: Matches ionization trends, where higher n approaches 0 eV (free electron).
Common errors include mistaking third excited as n=3 (-3.06 eV) or positive values, but the negative sign reflects bound state energy.
Exam Relevance
For CSIR NET, this tests atomic structure alongside molecular biology applications like spectroscopy in biotech. Practice transitions: from n=4 to n=1 emits 12.75 eV photon.
Quick Reference Table
| State | n Value | Energy (eV) |
|---|---|---|
| Ground | 1 | -13.60 |
| 1st Excited | 2 | -3.40 |
| 2nd Excited | 3 | -1.51 |
| 3rd Excited | 4 | -0.85 |
CSIR NET Preparation Tips
- Memorize the formula En = -13.6/n2 eV
- Always count excited states correctly: 3rd excited = n=4
- Negative sign indicates bound state energy
- Practice spectral line calculations
