Hydrogen Spectra: Spectral series (Lyman, Balmer, Paschen, Brackett, Pfund) and energy level diagrams

📘 Topic Description

The hydrogen spectrum is a line spectrum produced when electrons in a hydrogen atom undergo transitions between different quantised energy levels.

When an electron moves from a higher energy level to a lower energy level, a photon is emitted.

hν = E_i − E_f

⭐ The hydrogen spectrum consists of different spectral series depending upon the final energy level of the electron.

⚛️ Hydrogen Energy Levels

For hydrogen atom, the energy of an electron in the nth orbit is:

E_n = −13.6/n² eV

• n = 1 → Ground state
• n = 2 → First excited state
• n = 3 → Second excited state
• n = 4 → Third excited state
• n = ∞ → Ionisation limit

As n increases, energy levels become closer and finally converge at the ionisation limit.

📐 Rydberg Formula

1/λ = R_H [1/n_f² − 1/n_i²]

• n_i = initial higher energy level
• n_f = final lower energy level
• R_H ≈ 1.097 × 10⁷ m⁻¹

For emission: n_i > n_f

🌈 Spectral Series of Hydrogen

Series	Final Level	Initial Levels	Region
⭐ Lyman	n = 1	2,3,4,...	Ultraviolet
🔵 Balmer	n = 2	3,4,5,...	Visible
🟣 Paschen	n = 3	4,5,6,...	Infrared
🟠 Brackett	n = 4	5,6,7,...	Infrared
🔴 Pfund	n = 5	6,7,8,...	Infrared

⭐ 1. Lyman Series

n_f = 1

Transitions: 2 → 1, 3 → 1, 4 → 1, 5 → 1...

The Lyman series lies in the ultraviolet region.

🔵 2. Balmer Series

n_f = 2

Transitions: 3 → 2, 4 → 2, 5 → 2, 6 → 2...

The Balmer series is mainly associated with the visible region.

First Balmer line: 3 → 2

🟣 3. Paschen Series

n_f = 3

Transitions: 4 → 3, 5 → 3, 6 → 3...

Region: Infrared

🟠 4. Brackett Series

n_f = 4

Transitions: 5 → 4, 6 → 4, 7 → 4...

Region: Infrared

🔴 5. Pfund Series

n_f = 5

Transitions: 6 → 5, 7 → 5, 8 → 5...

Region: Infrared

🎬 Animated Hydrogen Energy-Level Diagram

Final Level n_f: 2

Initial Level n_i: 5

📊 Series-Wise Rydberg Equations

Lyman: 1/λ = R_H(1 − 1/n_i²)

Balmer: 1/λ = R_H(1/4 − 1/n_i²)

Paschen: 1/λ = R_H(1/9 − 1/n_i²)

Brackett: 1/λ = R_H(1/16 − 1/n_i²)

Pfund: 1/λ = R_H(1/25 − 1/n_i²)

📋 Important Comparison

Series	nf	First Transition	Region
Lyman	1	2 → 1	UV
Balmer	2	3 → 2	Visible
Paschen	3	4 → 3	IR
Brackett	4	5 → 4	IR
Pfund	5	6 → 5	IR

📝 MCQ Practice — 15 Questions

1. Lyman series corresponds to transitions ending at:

A. n = 1

B. n = 2

C. n = 3

D. n = 4

✔ Answer: A

2. Balmer series lies mainly in:

A. Infrared

B. Visible

C. Microwave

D. Gamma

✔ Answer: B

3. Paschen series terminates at:

A. n = 1

B. n = 2

C. n = 3

D. n = 4

✔ Answer: C

4. Brackett series terminates at:

A. n = 2

B. n = 3

C. n = 4

D. n = 5

✔ Answer: C

5. Pfund series terminates at:

A. n = 3

B. n = 4

C. n = 5

D. n = 6

✔ Answer: C

6. First Balmer line is due to:

A. 2 → 1

B. 3 → 2

C. 4 → 3

D. 5 → 4

✔ Answer: B

7. First Lyman line is:

A. 2 → 1

B. 3 → 2

C. 4 → 2

D. 3 → 1

✔ Answer: A

8. Paschen series lies in:

A. UV

B. Visible

C. Infrared

D. X-rays

✔ Answer: C

9. Approximate value of Rydberg constant is:

A. 1.097 × 10⁷ m⁻¹

B. 9.8 m/s²

C. 3 × 10⁸ m/s

D. 6.63 × 10⁻³⁴ J s

✔ Answer: A

10. When an electron moves from n = 5 to n = 2:

A. Energy is absorbed

B. Energy is emitted

C. No energy change

D. Atom is ionised

✔ Answer: B

11. Which has the shortest wavelength for the same initial level?

A. Lyman

B. Balmer

C. Paschen

D. Pfund

✔ Answer: A

12. Which transition belongs to Paschen series?

A. 3 → 2

B. 4 → 3

C. 5 → 4

D. 2 → 1

✔ Answer: B

13. Which transition belongs to Brackett series?

A. 4 → 3

B. 5 → 4

C. 6 → 5

D. 3 → 2

✔ Answer: B

14. Which transition belongs to Pfund series?

A. 5 → 4

B. 6 → 5

C. 4 → 2

D. 3 → 1

✔ Answer: B

15. Spectral lines are produced because:

A. Electrons have continuous energies

B. Electrons jump between quantised energy levels

C. Protons emit electrons

D. Nucleus disappears

✔ Answer: B

🟣 Assertion–Reason — 5 Questions

A. Both A and R are true and R is the correct explanation.
B. Both A and R are true but R is not the correct explanation.
C. A is true but R is false.
D. A is false but R is true.

1. Assertion: Hydrogen spectrum is a line spectrum.

Reason: Electrons occupy quantised energy levels.

Answer: A

2. Assertion: Balmer series contains visible lines.

Reason: Balmer transitions terminate at n = 2.

Answer: B

3. Assertion: Lyman series has shorter wavelength than Balmer series.

Reason: Lyman transitions involve larger energy differences.

Answer: A

4. Assertion: Paschen series is ultraviolet.

Reason: Paschen transitions terminate at n = 3.

Answer: D

5. Assertion: Spectral lines converge near series limit.

Reason: Energy levels become closer at higher n.

Answer: A

🟢 2 Marks — 6 Questions

Q1. What is meant by hydrogen spectrum?

Q2. State the Rydberg equation.

Q3. What is Lyman series?

Q4. What is Balmer series?

Q5. Which hydrogen series lies in visible region?

Q6. What is meant by series limit?

🟡 3 Marks — 6 Questions

Q1. Explain formation of spectral lines in hydrogen atom.

Q2. Explain Lyman and Balmer series.

Q3. Write all major hydrogen spectral series with final levels.

Q4. Why do spectral lines converge?

Q5. State relation between wavelength and photon energy.

Q6. State the significance of Rydberg constant.

🟠 4 Marks — 6 Questions

Q1. Derive Rydberg formula using Bohr's model.

Q2. Explain five major spectral series.

Q3. Draw and explain hydrogen energy-level diagram.

Q4. Explain Balmer series with first three transitions.

Q5. Explain series limit and its significance.

Q6. Compare Lyman, Balmer and Paschen series.

🔴 5 Marks — 6 Questions

Q1. Explain origin of hydrogen spectrum using Bohr model.

Q2. Derive Rydberg formula for hydrogen spectrum.

Q3. Explain Lyman, Balmer, Paschen, Brackett and Pfund series.

Q4. Draw energy-level diagram and explain spectral transitions.

Q5. Why do spectral lines become closer near series limit?

Q6. Derive wavelength expression for transition n_i → n_f.

🔵 6 Marks — 6 Questions

Q1. Explain hydrogen spectrum in detail and discuss all five spectral series.

Q2. Derive Rydberg formula from Bohr's atomic model.

Q3. Draw complete hydrogen energy-level diagram and explain all major transitions.

Q4. Explain spectral lines, series limit and convergence.

Q5. Compare all hydrogen spectral series on the basis of final level and region.

Q6. Explain how hydrogen spectrum supports quantisation of atomic energy.

🧮 Numerical Practice — 6 Questions

Q1. Calculate the wavelength emitted when an electron jumps from n = 3 to n = 2.

Q2. Calculate the wavelength of the first Lyman line.

Q3. Find the frequency for transition n = 4 → n = 2.

Q4. Identify the spectral series for transition n = 5 → n = 3.

Q5. Calculate photon energy for transition n = 4 → n = 2.

Q6. An electron falls from n = 6 to n = 1. Identify the series and calculate the wavelength using Rydberg equation.

🧠 High-Level Competitive Practice

Q1. An electron transitions from n = 6 to n = 2. Identify the spectral series and region.

Q2. Compare photon energies of transitions 4 → 2 and 4 → 3.

Q3. Which gives shorter wavelength: 5 → 1 or 5 → 2? Explain.

Q4. If wavelength decreases, what happens to photon frequency and energy?

Q5. How can the initial energy level be determined if final level and wavelength are known?

Q6. Why are hydrogen spectral lines not equally spaced in wavelength?

📌 One-Minute Formula Revision

Energy

E_n = −13.6/n² eV

Photon

E = hν = hc/λ

Rydberg

1/λ = R_H (1/n_f² − 1/n_i²)

Lyman

n_f = 1

Balmer

n_f = 2

Paschen

n_f = 3

Brackett

n_f = 4

Pfund

n_f = 5

🚀 One-Minute Revision

🔹 Hydrogen spectrum is a line spectrum.
🔹 Spectral lines arise due to transitions between quantised energy levels.
🔹 Lyman → n_f = 1 → UV.
🔹 Balmer → n_f = 2 → Visible.
🔹 Paschen → n_f = 3 → IR.
🔹 Brackett → n_f = 4 → IR.
🔹 Pfund → n_f = 5 → IR.
🔹 Higher → lower level gives photon emission.
🔹 Shorter wavelength means higher photon energy.
🔹 Spectral lines converge because energy-level separation decreases at higher n.

🔥 Important Exam Keywords

Hydrogen Spectra Hydrogen Spectrum Lyman Series Balmer Series Paschen Series Brackett Series Pfund Series Rydberg Formula Hydrogen Energy Levels Energy Level Diagram Hydrogen Atom Spectrum Class 12 Physics CBSE Physics JEE Physics NEET Physics

📚 Class 12 Physics • CBSE • JEE • NEET
🌈 Hydrogen Spectra • Lyman • Balmer • Paschen • Brackett • Pfund