#Rutherford model

De Broglie Hypothesis and Quantization in Bohr Model

In Rutherford’s model, what is the ratio of the size of the nucleus to the size of the atom if the nuclear radius is \(

**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. Ratio = (nuclear radius/atomic radius) = (10⁻¹⁵/10⁻¹⁰) = 10⁻⁵ . 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 10⁻⁵, consistent with Bohr

Ref: NCERT > Physics Book > Atoms and Nuclei > De Broglie Hypothesis and Quantization in Bohr Model

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Bohr Model Energy Levels and Hydrogen Spectrum

What assumption in Rutherford’s model contradicts classical electromagnetic theory?

**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. Rutherford assumes electrons orbit the nucleus like planets, but classical theory predicts they would radiate energy and collapse, not remain stable. Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE = Δm

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

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Atomic Models - Rutherford, Thomson and Bohr

What is the primary reason Rutherford’s model could not explain the line spectra of atoms?

**Rutherford's nuclear model** atom has small massive positively charged nucleus with electrons orbiting, size ratio atomic to nuclear ~10⁵, nucleus ~10⁻¹⁵ m atom ~10⁻¹⁰ m, most alpha particles with large impact parameter pass undeflected, small fraction >90° scatter from close approach, centripetal force provided by Coulomb attraction k Z e²/r², fails to explain stability because accelerating charge should radiate and collapse. Rutherford’s model lacks quantized energy levels, predicting continuous radiation as electrons accelerate, not discrete spectral lines. Using E_n = -13.6/n² eV, r_n =

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

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Atomic Models - Rutherford, Thomson and Bohr

In Rutherford’s model, what is the primary force keeping electrons in orbit around the nucleus?

**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. The electrostatic force of attraction between the positively charged nucleus and negatively charged electrons provides the centripetal force for orbiting. Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹

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

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Atomic Models - Rutherford, Thomson and Bohr

In Rutherford’s model, what provides the centripetal force for an electron orbiting the nucleus in a hydrogen atom?

**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. The electrostatic force between the electron and nucleus provides the centripetal force: (e²/4πepsilon₀ r²) = (m v²/r) . 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

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

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Atomic Models - Rutherford, Thomson and Bohr

In Rutherford’s model, what is the order of magnitude of the ratio of the atomic size to the nuclear size?

**Rutherford's nuclear model** atom has small massive positively charged nucleus with electrons orbiting, size ratio atomic to nuclear ~10⁵, nucleus ~10⁻¹⁵ m atom ~10⁻¹⁰ m, most alpha particles with large impact parameter pass undeflected, small fraction >90° scatter from close approach, centripetal force provided by Coulomb attraction k Z e²/r², fails to explain stability because accelerating charge should radiate and collapse. Atomic size ≈ 10⁻¹⁰ m , nuclear size ≈ 10⁻¹⁵ m . Ratio = (10⁻¹⁰/10⁻¹⁵) = 10⁵ . 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 > Atomic Models - Rutherford, Thomson and Bohr

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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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