Bohr model

Bohr’s Atomic Theory: Rectifying Rutherford’s Drawbacks

While Rutherford’s atomic model introduced the nucleus and the concept of electrons revolving around it, it could not explain the stability of the atom or the emission of discrete spectral lines. To overcome these limitations, Danish physicist Niels Bohr proposed a new atomic model in 1913, combining classical and quantum ideas.

Drawbacks of Rutherford’s Model

• Classical physics suggests that electrons in circular motion should lose energy over time and eventually collapse into the nucleus, implying atomic instability — which contradicts the observed stability of atoms.
• It also failed to provide a satisfactory explanation for the discrete spectral lines seen in hydrogen and other elements.

Bohr’s Postulates

1. Quantized Orbits: Electrons revolve around the nucleus in fixed circular paths called orbits or energy levels, without radiating energy. These orbits are associated with discrete energy values.
2. Energy Absorption and Emission: Electrons can jump from one orbit to another. Electrons gain energy to jump to higher energy levels and release energy when they return to lower levels. This released energy is emitted as electromagnetic radiation.
3. Angular Momentum Quantization: The angular momentum of an electron in orbit is quantized and given by the formula:
   mvr = nℏ, where:
   • m = mass of electron
   • v: represents the speed of the electron in its orbit
   • r: denotes the radius of the electron’s circular path
   • n = principal quantum number (1, 2, 3, ...)
   • ℏ = h / 2π, Planck’s constant divided by 2π

Explanation of Atomic Stability

Bohr’s theory accounted for atomic stability by suggesting that electrons travel in specific permitted orbits without emitting energy. This prevents them from losing energy and collapsing into the nucleus, ensuring the atom remains stable.

Formation of Line Spectrum

Bohr's model also clarified the origin of hydrogen's line spectra. When an electron jumps between energy levels, it either releases or absorbs a photon with a definite amount of energy:

ΔE = E_high - E_low = hν

This energy corresponds to a specific frequency (ν) of light, giving rise to discrete lines in the atomic emission spectrum. In the case of hydrogen, visible spectral lines observed in the Balmer series result from electrons falling to the second energy level.

Bohr’s atomic theory successfully explained the stability of atoms and the origin of atomic spectra, particularly for hydrogen. Though later refined by quantum mechanical models, it laid the foundation for modern atomic physics.