Atomic Models - Rutherford, Thomson and Bohr

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 = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE = Δm c² and 1 u = 931.5 MeV, evaluation

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Atomic Models - Rutherford, Thomson and Bohr

Which of the following statements is correct about the ionization energy of a hydrogen atom in Bohr’s model?

**Bohr's stationary orbits** defined by angular momentum quantization L = n ħ, ħ = h/2π, n=1 ground state, electron in these orbits does not radiate despite acceleration, contrary to classical EM theory which predicts atom collapse due to energy loss via radiation, Bohr postulates to explain observed stability and discrete spectra. The ionization energy is the energy required to remove the electron from the ground state ( n = 1 , -13.6 eV) to infinity (0 eV), which is 13.6 eV. 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

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Atomic Models - Rutherford, Thomson and Bohr

In Bohr’s model, what prevents an electron from emitting radiant energy while revolving in a stable orbit?

**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. Bohr’s first postulate states that electrons in certain stable orbits (stationary states) do not emit radiant energy, contrary to classical electromagnetic theory. 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

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Atomic Models - Rutherford, Thomson and Bohr

Why does the Bohr model predict discrete spectral lines for hydrogen?

**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. Discrete spectral lines arise because electrons transition between fixed energy levels, emitting photons with energies equal to the differences between these levels. Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE = Δm c² and

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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^¹/³, BE = Δm c² and 1 u = 931.5 MeV, evaluation yields Electrostatic force,

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Atomic Models - Rutherford, Thomson and Bohr

What is the wavelength of a photon emitted when an electron drops from \( n = 4 \) to \( n = 3 \) in a hydrogen atom? (U

**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. Δ E = 0.66 eV = 1.056 × 10⁻¹⁹ J . λ = (hc/Δ E) = (6.6 × 10⁻³⁴ × 3 × 10⁸/1.056 × 10⁻¹⁹) ≈ 1.875 × 10⁻⁶ m . Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE = Δm

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Atomic Models - Rutherford, Thomson and Bohr

A hydrogen atom in the \( n = 5 \) state emits a photon and returns to the ground state. What is the maximum energy of t

**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. E₅ = -0.544 eV , E₁ = -13.6 eV . Δ E = -0.544 - (-13.6) = 13.056 eV ≈ 13.06 eV . 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

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Atomic Models - Rutherford, Thomson and Bohr

Which of the following statements is correct about the energy levels in a hydrogen atom according to Bohr’s model?

**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. The energy becomes less negative (increases) as the principal quantum number n increases, approaching zero at n = ∞ . 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

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Atomic Models - Rutherford, Thomson and Bohr

The radius of the first orbit in a hydrogen atom is \( 5.3 \times 10^{-11} \, \text{m} \). What is the radius of the sec

**Bohr's stationary orbits** defined by angular momentum quantization L = n ħ, ħ = h/2π, n=1 ground state, electron in these orbits does not radiate despite acceleration, contrary to classical EM theory which predicts atom collapse due to energy loss via radiation, Bohr postulates to explain observed stability and discrete spectra. Radius r_n = n² r₁ , where r₁ = 5.3 × 10⁻¹¹ m . For n = 2 : r₂ = 2² × 5.3 × 10⁻¹¹ = 4 × 5.3 × 10⁻¹¹ = 2.12 × 10⁻¹⁰ m . Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀

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Atomic Models - Rutherford, Thomson and Bohr

Which of the following statements is correct about Thomson’s model of the 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. Thomson’s model describes the atom as a sphere of positive charge with electrons embedded in it, resembling a plum pudding, not a nuclear structure. 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,

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Atomic Models - Rutherford, Thomson and Bohr

What is the wavelength of the photon emitted when an electron in a hydrogen atom drops from \( n = 3 \) to \( n = 2 \)?

**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. E₃ = -1.51 eV , E₂ = -3.4 eV . Δ E = 1.89 eV = 1.89 × 1.6 × 10⁻¹⁹ = 3.024 × 10⁻¹⁹ J . λ = (hc/Δ E) = (6.6 × 10⁻³⁴ × 3 × 10⁸/3.024 × 10⁻¹⁹) ≈ 6.56 ×

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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, evaluation yields Electrostatic force, consistent with

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