#alpha particles

De Broglie Hypothesis and Quantization in Bohr Model

In Rutherford’s scattering experiment, what does the small number of alpha-particles undergoing head-on collisions sugge

**Quantization basis** de Broglie standing wave requires constructive interference, integer wavelengths in orbit, otherwise destructive, so only certain radii allowed r_n = n² a₀, a₀=0.53 Å, angular momentum L = n h/2π, de Broglie explains why orbits are stationary - electron wave closed on itself. The rarity of head-on collisions (1 in 8000 rebounding back) suggests that the nucleus, containing most of the mass and charge, is very small compared to the atom. 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 Nucleus occupies a

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Bohr Model Energy Levels and Hydrogen Spectrum

What is the role of the impact parameter in Rutherford’s alpha-particle scattering?

**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. The impact parameter determines the scattering angle; a smaller impact parameter leads to a larger deflection due to closer approach to the nucleus. 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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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

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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.

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Bohr Model Energy Levels and Hydrogen Spectrum

In Rutherford’s scattering experiment, what does a small fraction of alpha-particles rebounding back 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. It indicates that the positive charge and most of the mass are concentrated in a small nucleus, causing strong repulsion in head-on collisions. Using E_n = -13.6/n² eV, r_n = n² a₀, L = n h/2π, R = R₀ A^¹/³, BE = Δm c² an

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Atomic Models - Rutherford, Thomson and Bohr

In Rutherford’s scattering experiment, what happens to an alpha-particle with a large impact parameter?

**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. For a large impact parameter, the alpha-particle experiences minimal deflection ( θ ≈ 0 ) and goes nearly undeviated. 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 Goes nearly undeviated, consistent

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