Structure of Atoms and Nuclei

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Thomson's atomic model (1903) proposed that an atom is a sphere with uniform positive charge in which negatively charged electrons are embedded like plums in a pudding. The total positive charge equal…

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Only about one alpha particle in 8000 (0.0125%) was deflected through angles larger than 90°. Most alpha particles (99.86%) passed straight through the gold foil with negligible deflection. Only 0.14%…

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1) According to Maxwell's equations, orbiting electrons should continuously emit electromagnetic radiation and lose energy. 2) The electron should spiral into the nucleus causing atomic collapse. 3) T…

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1/λ = RH(1/n² - 1/m²), where λ is wavelength of spectral line, RH = 1.097 × 10⁷ m⁻¹ is Rydberg constant, n = 1,2,3... for Lyman, Balmer, Paschen series respectively, and m takes integral values greate…

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1) Electrons revolve around nucleus in circular orbits with centripetal force provided by electrostatic attraction. 2) Angular momentum of electron is quantized: mvr = nh/2π, where n is principal quan…

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Using the formula rn = a₀n², where a₀ = 0.053 nm is the Bohr radius: r₃ = a₀ × 3² = a₀ × 9 = 0.053 × 9 = 0.477 nm The general formula is rn = (n²h²ε₀)/(πmeZe²) for hydrogen-like atoms, which simplifi…

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En = -13.6Z²/n² eV. For hydrogen (Z=1): En = -13.6/n² eV. Ground state (n=1): E₁ = -13.6 eV First excited state (n=2): E₂ = -3.4 eV Second excited state (n=3): E₃ = -1.51 eV Negative energy indicate…

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When the alpha particle stops, all kinetic energy converts to potential energy: K = (1/4πε₀) × (Zαe)(ZAue)/r For gold: ZAu = 79, Zα = 2 Using K = 9×10⁹ × (2×79×(1.6×10⁻¹⁹)²)/r 28.33 MeV = 28.33 × 1.6…