Bohr model energy levels: Class 12 practice
In the Bohr model of hydrogen, Eₙ = −13.6/n² eV and rₙ = 0.529n² Å. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Fractions
The idea behind bohr model energy levels
In the Bohr model of hydrogen, Eₙ = −13.6/n² eV and rₙ = 0.529n² Å. A jump from n₂ to n₁ emits a photon of energy E = 13.6(1/n₁² − 1/n₂²) eV and wavelength λ = 1240/E nm.
Step-by-step method
- Eₙ = −13.6/n².
- Photon energy = difference between levels.
- λ (nm) = 1240/E (eV).
Worked example 1 (Basic)
Find the energy and radius of the n = 2 orbit of hydrogen.
- Eₙ = −13.6/4 = -3.4 eV
- rₙ = 0.529 × 4 = 2.116 Å
- Answer: -3.4 eV, 2.116 Å
Worked example 2 (Standard)
Find the energy of the photon emitted when hydrogen's electron falls from n = 5 to n = 3.
- E = 13.6(1/9 − 1/25)
- = 0.967 eV
- Answer: 0.967 eV
Worked example 3 (Challenge)
Find the ionisation energy of hydrogen from the n = 4 level.
- E = 0 − (−13.6/16)
- = 0.85 eV
- Answer: 0.85 eV
Common mistakes and misconceptions
- Sign errors with negative energies
- Using n instead of n²
Practice questions
- (Basic) Find the energy and radius of the n = 5 orbit of hydrogen.
- (Basic) Find the energy and radius of the n = 3 orbit of hydrogen.
- (Standard) Find the energy of the photon emitted when hydrogen's electron falls from n = 4 to n = 2.
- (Standard) Find the energy of the photon emitted when hydrogen's electron falls from n = 3 to n = 1.
- (Challenge) Find the ionisation energy of hydrogen from the n = 6 level.
- (Challenge) Find the ionisation energy of hydrogen from the n = 3 level.
Answer key with full working
- Q1: Eₙ = −13.6/25 = -0.544 eV → rₙ = 0.529 × 25 = 13.225 Å → Answer: -0.544 eV, 13.225 Å
- Q2: Eₙ = −13.6/9 = -1.511 eV → rₙ = 0.529 × 9 = 4.761 Å → Answer: -1.511 eV, 4.761 Å
- Q3: E = 13.6(1/4 − 1/16) → = 2.55 eV → Answer: 2.55 eV
- Q4: E = 13.6(1/1 − 1/9) → = 12.089 eV → Answer: 12.089 eV
- Q5: E = 0 − (−13.6/36) → = 0.378 eV → Answer: 0.378 eV
- Q6: E = 0 − (−13.6/9) → = 1.511 eV → Answer: 1.511 eV
Syllabus note
This skill is listed under "Atoms" for Class 12 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is bohr model energy levels in?
"Atoms", Class 12 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.