Bohr’s Model of the Atom

Bohr’s Model of the Atom

Illustration of Bohr’s atomic model showing quantized electron orbits around a nucleus.

The Bohr model, proposed by Niels Bohr in 1913, introduced quantized electron orbits and explained the discrete spectral lines of hydrogen. Below is a clear, exam-ready summary with formulas, examples and practice items.

1. Key Postulates of Bohr’s Model

• Electrons move in fixed circular orbits (stationary states) without radiating energy.
• Each allowed orbit has a specific quantized energy.
• An electron emits or absorbs a photon when it jumps between orbits with energy difference ΔE = Em − En.
• Angular momentum is quantized: mvr = n(h/2π), where n = 1,2,3,…

2. Radius & Energy of Orbits (Important formulas)

Radius of nth orbit: r_n = n² × r₁ = n² × 0.529 Å
Energy of nth orbit: E_n = −13.6 eV / n²

Here r₁ = 0.529 Å (Bohr radius). n is the principal quantum number (n = 1,2,3,…).

3. Explanation of Atomic Spectra

When an electron transitions from an orbit with quantum number m to a lower orbit n, the emitted photon energy is:

E = E_m − E_n = 13.6 eV × (1/n² − 1/m²)

This equation explains hydrogen spectral series (Lyman, Balmer, Paschen, etc.).

4. Limitations of Bohr’s Model

• Works well only for hydrogen-like (single-electron) atoms.
• Fails for multi-electron atoms—doesn’t consider electron-electron interactions.
• Cannot explain fine structure, electron spin, or Zeeman/Stark effects.
• Replaced by the quantum mechanical model (wave mechanics) for a full description.

5. Importance & Legacy

Despite limitations, Bohr’s model introduced quantization to atomic theory and paved the way for quantum mechanics. Its simple formulas remain useful for calculations involving hydrogen-like species.

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Fill in the blanks (answers below)

1. The angular momentum in Bohr’s model is quantized as mvr = n × (h/2π). (Answer: n(h/2π))
2. The energy of the nth orbit is given by E_n = ____ eV / n². (Answer: −13.6)
3. The Bohr radius (r₁) is approximately ____ Å. (Answer: 0.529)

Quiz: Bohr’s Model

Q1: What does Bohr’s model say about the energy of electrons?
A) Continuous energy values
B) Random energies
C) Quantized energy levels
D) No energy

Answer: C) Quantized energy levels.
Explanation: Electrons occupy fixed energy orbits and energy differences give photon frequencies.

Q2: When does an electron emit a photon?
A) Moving in fixed orbit
B) Jumping to a higher orbit
C) Jumping to a lower orbit
D) Orbiting faster only

Answer: C) Jumping from higher to lower orbit.
Explanation: The photon energy equals the difference between initial and final energy levels.

Q3: The radius of the first Bohr orbit is approx:
A) 0.53 nm
B) 0.53 Å
C) 1.06 Å
D) 1.06 nm

Answer: B) 0.53 Å.
Explanation: Bohr radius ≈ 0.529 angstroms.

Q4: Bohr’s model cannot explain:
A) Hydrogen spectral lines
B) Atomic number
C) Fine structure and Zeeman effect
D) Energy quantization

Answer: C) Fine structure and Zeeman effect.
Explanation: These require relativistic and spin considerations absent in Bohr’s model.

Further reading: Wikipedia: Bohr model · internal: Atomic Models.

Last reviewed: Sep 2025 · Author: CHEMASH