Atomic and Nuclear physics

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Specific charge is the charge per unit mass of an electron. Value: e/m = 1.7 × 10¹¹ C/kg In Thomson's experiment: • Cathode rays passed through crossed electric (E) and magnetic (B) fields • When fo…

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Given: m = 1.6 × 10⁻¹⁵ kg, E = 1000 V/cm = 10⁵ V/m, g = 10 m/s² At equilibrium, electric force balances weight: qE = mg Step 1: Calculate gravitational force F_g = mg = 1.6 × 10⁻¹⁵ × 10 = 1.6 × 10⁻¹…

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Thomson's Model (Watermelon Model): • Positive charge uniformly distributed with electrons embedded • Drawback: Could not explain atom stability; violated Earnshaw's theorem Rutherford's Model (Nucle…

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Angular Momentum Quantization: Condition: L = mvr = nℏ = n(h/2π) Where: • L = angular momentum • m = electron mass • v = electron velocity • r = orbital radius • n = principal quantum number (1, 2, 3…

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Given: n = 3, a₀ = 0.529 Å = 0.529 × 10⁻¹⁰ m, Z = 1 (hydrogen) Formula: r_n = (a₀ × n²)/Z Step 1: Substitute values r₃ = (0.529 × 3²)/1 Å r₃ = (0.529 × 9) Å r₃ = 4.761 Å Step 2: Convert to meters r…

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Formula: v_n = (αcZ)/n where α = fine structure constant = 1/137 For hydrogen ground state: n = 1, Z = 1 Step 1: Calculate velocity v₁ = (c × 1)/(137 × 1) v₁ = (3 × 10⁸)/137 v₁ = 2.19 × 10⁶ m/s Ste…

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Formula: ΔE = E_f - E_i = -13.6 Z²(1/n_f² - 1/n_i²) eV Given: Z = 1 (hydrogen), n_i = 1, n_f = 3 Step 1: Calculate final and initial energies E₁ = -13.6 × 1²/1² = -13.6 eV E₃ = -13.6 × 1²/3² = -13.6…

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Ionization Energy (from ground state): E_ionization = E_∞ - E₁ = 0 - (-13.6 eV) = 13.6 eV General Formula: E_ion = 13.6 Z²/n² eV Why this specific value: 1. Energy Zero Reference: Zero energy is as…