Bohr's Atomic Theory
1️⃣ Bohr’s Postulates (Core Assumptions)
Postulate 1 — Stationary Orbits
Electrons move only in certain fixed circular orbits around the nucleus.
Meaning:
An electron is allowed to move only in specific paths called stationary states.
---
Postulate 2 — No Radiation in Allowed Orbits
While an electron is in a stationary orbit, it does not emit or absorb energy.
Meaning:
Energy loss does not happen in allowed orbits → atom remains stable.
---
Postulate 3 — Quantization of Angular Momentum
m v r = n h / 2π
where:
m = mass of electron
v = velocity
r = radius of orbit
n = orbit number (1, 2, 3, …)
h = Planck’s constant
Meaning:
Electron’s angular momentum is not continuous; it is quantized.
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Postulate 4 — Emission/Absorption During Transitions
ΔE = E₂ − E₁ = hν
Meaning:
Radiation is emitted or absorbed only when an electron jumps between orbits.
2️⃣
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EXAM-Oriented Results from Bohr Theory
(a) Radius of nth Orbit (Hydrogen)
rₙ = n² a₀
where a₀ = 0.529 Å (Bohr radius)
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(b) Energy of nth Orbit (Hydrogen)
Eₙ = −13.6 / n² eV
✔ n = 1 → Ground state → −13.6 eV
✔ n → ∞ → E → 0 (ionization)
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(c) Velocity of Electron
vₙ = 2.18 × 10⁶ / n m/s (for hydrogen)
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(d) Frequency of Spectral Line
ν = (E₂ − E₁) / h
3️⃣
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Detailed Explanation (Concept Logic)
🔹 Why Bohr Model Was Needed
Rutherford’s model failed because:
,• According to classical physics, moving electrons should radiate energy and fall into nucleus
• But atoms are stable
Bohr fixed this by introducing quantization.
🔹
---
Stability of Atom
Electron in a stationary orbit:
✔ Does NOT radiate
✔ Has fixed energy
So, no energy loss → no collapse → atom is stable.
🔹
---
Spectral Lines Explanation
When electron jumps:
• From higher orbit → lower → emission
• From lower orbit → higher → absorption
Each jump gives a photon of specific frequency → line spectrum.
4️⃣❌Limitations of Bohr’s Theory
1. Works Only for Hydrogen-like Atoms
Fails for multi-electron atoms (He, Li, etc.).
❌ 2. Cannot Explain Zeeman Effect
Splitting of spectral lines in magnetic field not explained.
❌ 3. Cannot Explain Stark Effect
Splitting of lines in electric field not explained.
❌ 4. Ignores Wave Nature of Electron
Electron behaves as both particle + wave (de Broglie).
❌ 5. Violates Heisenberg Uncertainty Principle
Bohr assumed exact:
• Position
• Momentum
• Path
which is not possible in quantum mechanics.
, De Brogli Wave
Dual Behaviour of Matter & Radiation
🔹 1. Classical View (Before Quantum Theory)
• Light was treated as a wave (interference, diffraction).
• Matter (electrons, particles) was treated as particles.
But experiments showed:
• Light also behaves like particles (photoelectric effect).
• Matter also behaves like waves (electron diffraction).
So both radiation and matter show dual nature.
🔹
---
2. Dual Nature of Radiation (Light)
From the Photoelectric Effect:
• Light ejects electrons from metal only if frequency is high enough
• Energy comes in packets (quanta) called photons
E = hν
where:
E = energy of photon
h = Planck’s constant
ν = frequency
✔ This proves: Light = Wave + Particle
🔹
---
3. de Broglie Hypothesis (Wave Nature of Matter)
In 1924, Louis de Broglie proposed:
> If light (radiation) can behave like a particle,
then matter (particles) should also behave like waves.
So every moving particle has an associated matter wave.
🔹
---
4. de Broglie Relation (Wavelength of a Particle)
λ=h/p
where:
λ = wavelength of matter wave
h = Planck’s constant
p = momentum of particle
Since
p = mv
λ = h / mv
1️⃣ Bohr’s Postulates (Core Assumptions)
Postulate 1 — Stationary Orbits
Electrons move only in certain fixed circular orbits around the nucleus.
Meaning:
An electron is allowed to move only in specific paths called stationary states.
---
Postulate 2 — No Radiation in Allowed Orbits
While an electron is in a stationary orbit, it does not emit or absorb energy.
Meaning:
Energy loss does not happen in allowed orbits → atom remains stable.
---
Postulate 3 — Quantization of Angular Momentum
m v r = n h / 2π
where:
m = mass of electron
v = velocity
r = radius of orbit
n = orbit number (1, 2, 3, …)
h = Planck’s constant
Meaning:
Electron’s angular momentum is not continuous; it is quantized.
---
Postulate 4 — Emission/Absorption During Transitions
ΔE = E₂ − E₁ = hν
Meaning:
Radiation is emitted or absorbed only when an electron jumps between orbits.
2️⃣
---
EXAM-Oriented Results from Bohr Theory
(a) Radius of nth Orbit (Hydrogen)
rₙ = n² a₀
where a₀ = 0.529 Å (Bohr radius)
---
(b) Energy of nth Orbit (Hydrogen)
Eₙ = −13.6 / n² eV
✔ n = 1 → Ground state → −13.6 eV
✔ n → ∞ → E → 0 (ionization)
---
(c) Velocity of Electron
vₙ = 2.18 × 10⁶ / n m/s (for hydrogen)
---
(d) Frequency of Spectral Line
ν = (E₂ − E₁) / h
3️⃣
---
Detailed Explanation (Concept Logic)
🔹 Why Bohr Model Was Needed
Rutherford’s model failed because:
,• According to classical physics, moving electrons should radiate energy and fall into nucleus
• But atoms are stable
Bohr fixed this by introducing quantization.
🔹
---
Stability of Atom
Electron in a stationary orbit:
✔ Does NOT radiate
✔ Has fixed energy
So, no energy loss → no collapse → atom is stable.
🔹
---
Spectral Lines Explanation
When electron jumps:
• From higher orbit → lower → emission
• From lower orbit → higher → absorption
Each jump gives a photon of specific frequency → line spectrum.
4️⃣❌Limitations of Bohr’s Theory
1. Works Only for Hydrogen-like Atoms
Fails for multi-electron atoms (He, Li, etc.).
❌ 2. Cannot Explain Zeeman Effect
Splitting of spectral lines in magnetic field not explained.
❌ 3. Cannot Explain Stark Effect
Splitting of lines in electric field not explained.
❌ 4. Ignores Wave Nature of Electron
Electron behaves as both particle + wave (de Broglie).
❌ 5. Violates Heisenberg Uncertainty Principle
Bohr assumed exact:
• Position
• Momentum
• Path
which is not possible in quantum mechanics.
, De Brogli Wave
Dual Behaviour of Matter & Radiation
🔹 1. Classical View (Before Quantum Theory)
• Light was treated as a wave (interference, diffraction).
• Matter (electrons, particles) was treated as particles.
But experiments showed:
• Light also behaves like particles (photoelectric effect).
• Matter also behaves like waves (electron diffraction).
So both radiation and matter show dual nature.
🔹
---
2. Dual Nature of Radiation (Light)
From the Photoelectric Effect:
• Light ejects electrons from metal only if frequency is high enough
• Energy comes in packets (quanta) called photons
E = hν
where:
E = energy of photon
h = Planck’s constant
ν = frequency
✔ This proves: Light = Wave + Particle
🔹
---
3. de Broglie Hypothesis (Wave Nature of Matter)
In 1924, Louis de Broglie proposed:
> If light (radiation) can behave like a particle,
then matter (particles) should also behave like waves.
So every moving particle has an associated matter wave.
🔹
---
4. de Broglie Relation (Wavelength of a Particle)
λ=h/p
where:
λ = wavelength of matter wave
h = Planck’s constant
p = momentum of particle
Since
p = mv
λ = h / mv
