Discuss the limitations of Rutherford's atomic model. Explain how Bohr's atomic model successfully overcame these limitations and accounted for the stability of atoms and atomic spectra.

Q: Discuss the limitations of Rutherford's atomic model. Explain how Bohr's atomic model successfully overcame these limitations and accounted for the stability of atoms and atomic spectra.

Limitations of Rutherford's Atomic Model\nAlthough Rutherford's $\alpha$-particle scattering experiment successfully established the nuclear model of the atom (proposing a heavy, positively charged nucleus surrounded by orbiting electrons), it suffered from major theoretical flaws: Inability to Explain Stability of Atom: According to classical electrodynamics (Maxwell's theory), any accelerated charged particle must continuously radiate electromagnetic energy. Since an electron revolving in a circular orbit experiences centripetal acceleration, it should continuously lose energy and spiral into the nucleus within a fraction of a second ($10^{-8}$ s). However, atoms are stable. Inability to Explain Line Spectra: According to Rutherford's model, electrons can revolve in any arbitrary orbit. Consequently, they should radiate a continuous spectrum of all frequencies. However, experiments with atomic gases show distinct line spectra (discrete frequencies). How Bohr's Model Overcame These Limitations\nNiels Bohr in 1913 proposed a new model that successfully resolved the shortcomings of Rutherford's model by introducing quantum postulates: Resolution of Stability: Bohr postulated that electrons do not radiate energy while revolving in certain specific non-radiating orbits called stationary orbits. Energy is only emitted or absorbed when an electron jumps between these fixed energy states. Resolution of Line Spectra: Since the permitted orbits have fixed, discrete energies ($En$), the energy difference $\Delta E = E2 - E1$ is also fixed. When an electron transitions from a higher orbit to a lower orbit, a photon of a specific, single frequency ($\nu = \Delta E / h$) is emitted, resulting in discrete line spectra rather than a continuous spectrum. \nThus, Bohr's model successfully bridged classical mechanics and early quantum theory to explain atomic stability and spectral series.

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Limitations of Rutherford's Atomic Model
Although Rutherford's $\alpha$-particle scattering experiment successfully established the nuclear model of the atom (proposing a heavy, positively charged nucleus surrounded by orbiting electrons), it suffered from major theoretical flaws: Inability to Explain Stability of Atom: According to classical electrodynamics (Maxwell's theory), any accelerated charged particle must continuously radiate electromagnetic energy. Since an electron revolving in a circular orbit experiences centripetal acceleration, it should continuously lose energy and spiral into the nucleus within a fraction of a second ($10^{-8}$ s). However, atoms are stable. Inability to Explain Line Spectra: According to Rutherford's model, electrons can revolve in any arbitrary orbit. Consequently, they should radiate a continuous spectrum of all frequencies. However, experiments with atomic gases show distinct line spectra (discrete frequencies). How Bohr's Model Overcame These Limitations
Niels Bohr in 1913 proposed a new model that successfully resolved the shortcomings of Rutherford's model by introducing quantum postulates: Resolution of Stability: Bohr postulated that electrons do not radiate energy while revolving in certain specific non-radiating orbits called stationary orbits. Energy is only emitted or absorbed when an electron jumps between these fixed energy states. Resolution of Line Spectra: Since the permitted orbits have fixed, discrete energies ($En$), the energy difference $\Delta E = E2 - E1$ is also fixed. When an electron transitions from a higher orbit to a lower orbit, a photon of a specific, single frequency ($
u = \Delta E / h$) is emitted, resulting in discrete line spectra rather than a continuous spectrum. 
Thus, Bohr's model successfully bridged classical mechanics and early quantum theory to explain atomic stability and spectral series.

CBSE · Class 12 · Physics · AtomsDiscuss the limitations of Rutherford's atomic model. Explain how Bohr's atomic model successfully overcame these limitations and accounted for the stability of atoms and atomic spectra.

Limitations of Rutherford's Atomic Model\nAlthough Rutherford's $\alpha$-particle scattering experiment successfully established the nuclear model of the atom (proposing a heavy, positively charged nucleus surrounded by orbiting electrons), it suffered from major theoretical flaws:

How Bohr's Model Overcame These Limitations\nNiels Bohr in 1913 proposed a new model that successfully resolved the shortcomings of Rutherford's model by introducing quantum postulates: