Developments Leading to the Bohr’s Atomic Model

Two key developments provided the foundation for Bohr's model:

(i) Wave-Particle Duality of Electromagnetic Radiation

Electromagnetic radiation has a dual nature — it behaves both as a wave and as a stream of particles called photons. Each photon carries energy:

where h = Planck's constant = 6.626 × 10⁻³⁴ J·s and ν = frequency.

Key wave properties:

• Wavelength (λ): Distance between two consecutive crests or troughs

• Frequency (ν): Number of waves passing a given point per second (unit: Hz or s⁻¹)

• Wave number \[(\bar{\nu})\]: Number of wavelengths per unit length = 1/λ (unit: cm⁻¹ or m⁻¹)

Relation between speed, frequency, and wavelength:

\[c=\nu\lambda\quad\Rightarrow\quad\nu=\frac{c}{\lambda}\]

Longer wavelength → smaller frequency → lower energy of radiation.

(ii) Quantisation of Energy

Results of atomic spectra showed that atoms absorb or emit energy only in discrete amounts. This gave evidence that energy is quantised — it comes in fixed packets (quanta).

Evolution of Quantum Theory (Timeline):

Classical Theory (matter = particles, radiation = waves)

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Einstein & Planck Energy is Quantised

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Bohr Line Spectra (Bohr's H atom model)

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de Broglie Matter has Wave Nature

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Heisenberg Uncertainty Principle

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Schrödinger Quantum Theory (matter & radiation both have wave-particle duality)