Write down the essential postulates of Bohr's model of atom. How did it explain the stability of an atom ?

Essential Postulates of Bohr’s Model of Atom

Niels Bohr proposed his atomic model in 1913 to explain the stability of atoms and the line spectra of hydrogen. The key postulates are:

1. Electrons revolve in fixed orbits (stationary states): Electrons move in circular orbits around the nucleus without radiating energy, unlike classical physics predictions. These orbits are called stationary states or energy levels, each with a fixed energy.

2. Quantization of energy levels: Only certain orbits with specific radii and energies are allowed. The energy of an electron in the nth orbit is given by: $$E_n=-\frac{13.6}{n^2}\text{ eV}$$ where n = 1, 2, 3, ... (principal quantum number).

3. Electrons emit/absorb energy only during transitions: An electron jumps from a higher energy level (n₂) to a lower one (n₁), emitting a photon of energy: $$\Delta E=E_{n_2}-E_{n_1}=h\nu =\frac{hc}{\lambda }$$ Conversely, absorption occurs when an electron moves to a higher orbit.

4. Angular momentum is quantized: The angular momentum (L) of an electron in an orbit is an integer multiple of $\frac{h}{2\pi }$: $$L=mvr=n\frac{h}{2\pi }$$ where m = electron mass, v = velocity, r = radius, and h = Planck’s constant.

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Explanation of Atomic Stability

Bohr’s model resolved the classical instability problem (electrons should lose energy and spiral into the nucleus) by introducing quantized orbits. Key points:

1. Discrete Energy Levels Prevent Collapse: Unlike classical physics, electrons do not continuously lose energy. They occupy fixed orbits where energy is quantized, preventing them from falling into the nucleus.

2. Stable Orbits via Centripetal Force: The electrostatic attraction between the nucleus and electron provides the centripetal force for circular motion: $$\frac{e^2}{4\pi {ϵ}_0{r}^2}=\frac{m{v}^2}{r}$$ Bohr derived the radius of the nth orbit as: $$r_n=n^2{a}_0(a_0=0.529\text{ A˚})$$ This ensures stable circular motion without radiation.

3. Quantum Jumps Explain Spectra: The stability of atoms is linked to their energy levels. Transitions between levels (e.g., n = 3 → n = 2) emit/absorb specific wavelengths, matching observed spectral lines (e.g., Balmer series for hydrogen).

4. Limitation: Applies Only to Hydrogen-like Atoms Bohr’s model works perfectly for single-electron systems (H⁺, He⁺) but fails for multi-electron atoms due to electron-electron repulsion. Later, quantum mechanics (Schrödinger’s wave model) generalized these ideas.

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Note: The model’s success in explaining hydrogen’s spectrum (e.g., $\lambda =656.3\text{ nm}$ for n = 3 → 2) validated its postulates, though it was later refined.