#nuclear model

De Broglie Hypothesis and Quantization in Bohr Model

What was the primary evidence from Rutherford’s alpha-particle scattering experiment that led to the nuclear model of th

**De Broglie hypothesis** λ = h/p, p=mv momentum, suggests electron as wave, in Bohr model circumference 2πr = n λ, standing wave condition, n wavelengths fit into orbit, for n=6, 6 wavelengths, for n=4, 4 wavelengths, explains quantization of angular momentum L = r p = r h/λ = r h n/(2πr)= n h/2π = n ħ, physical basis for Bohr quantization. The observation that a small fraction of alpha-particles were deflected by large angles (e.g., more than 90°) indicated a small, dense, positively charged nucleus at the atom’s center. Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R =

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Bohr Model Energy Levels and Hydrogen Spectrum

In Rutherford’s nuclear model, why do most alpha-particles pass through the gold foil without deflection?

**Excitation** energy required to go from n=1 to n=3 is 12.09 eV, from ground to n=∞ ionization 13.6 eV, state n=∞ means ionized, electron free with zero energy, highest level reached by electron beam energy determines which levels can be excited, e.g., 11 eV beam from ground can reach n=2 (10.2 eV) but not n=3 (12.09 eV), so max n=2. Most of the atom is empty space, with the nucleus occupying a very small volume, so most alpha-particles do not encounter the nucleus and pass through undeflected. Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE

Ref: NCERT > Physics Book > Atoms and Nuclei > Bohr Model Energy Levels and Hydrogen Spectrum

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Bohr Model Energy Levels and Hydrogen Spectrum

In Rutherford’s experiment, what does the scattering of alpha-particles at small angles indicate?

**Bohr energy levels** E_n = -13.6/n² eV for hydrogen, negative indicating bound state, total energy = -13.6 eV ground state n=1, -3.4 eV n=2, -1.51 eV n=3, etc., photon energy for transition n_i → n_f is ΔE =13.6(1/n_f² -1/n_i²) eV, wavelength λ = hc/ΔE, h=6.6×10⁻³⁴ J·s, c=3×10⁸ m/s. Emission line spectrum characterized by discrete wavelengths because energy levels discrete. Small-angle scattering occurs when alpha-particles pass far from the nucleus (large impact parameter), experiencing weak repulsion. Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE = Δm c² and 1 u = 931.

Ref: NCERT > Physics Book > Atoms and Nuclei > Bohr Model Energy Levels and Hydrogen Spectrum

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Atomic Models - Rutherford, Thomson and Bohr

Why did Rutherford’s nuclear model fail to explain the stability of atoms?

**Thomson's plum pudding model** positive charge uniformly distributed in sphere with electrons embedded, positive charge spread, fails to explain large angle scattering observed. Bohr's model introduces stationary orbits with quantized angular momentum L = n h/2π, physical basis de Broglie standing wave condition 2πr = n λ, circumference fits n wavelengths, explains line spectrum. In classical theory, an accelerating electron (in circular orbit) emits radiation, losing energy and spiraling into the nucleus, contradicting atomic stability. Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R =

Ref: NCERT > Physics Book > Atoms and Nuclei > Atomic Models - Rutherford, Thomson and Bohr

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Radioactive Decay, Nuclear Forces and Stability

Which of the following statements is incorrect about Rutherford’s nuclear model?

**Stability** belt of stability N≈Z for light, N>Z for heavy due to Coulomb, beyond leads to alpha decay, fission, stability requires balance, nuclear force saturated explains constant density and BE/A. Rutherford’s model does not explain atomic stability, as it predicts electrons would emit radiation and collapse into the nucleus, not maintain stable orbits. Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE = Δm c² and 1 u = 931.5 MeV, evaluation yields Electrons maintain stable orbits without radiating, consistent with Bohr model and nuclear binding energy systematics.

Ref: NCERT > Physics Book > Atoms and Nuclei > Radioactive Decay, Nuclear Forces and Stability

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