Govt. Exams
Entrance Exams
Using Compton scattering formula: λ' - λ = (h/mₑc)(1 - cos θ). With given values, the wavelength shift is 2.4 pm. Using energy conservation, the incident photon energy is E₀ = hc/λ ≈ 12.4 keV. The scattered photon energy E' = hc/λ' ≈ 12.1 keV. The kinetic energy of electron = E₀ - E' ≈ 1.65 keV.
For heavy nuclei, the Coulomb repulsion between protons increases significantly. Extra neutrons (uncharged) help stabilize the nucleus without increasing repulsion, requiring N > Z for stability.
11,460 years = 2 × 5730 years = 2 half-lives. After 2 half-lives: 1 × (1/2)² = 0.25 mg remains.
In pair production: E_photon = 2m_e c² + KE_total. Excess = 3 - 2(0.51) = 1.98 MeV becomes kinetic energy of the pair.
Possible transitions: 3→1 (direct), 3→2, 2→1. Total = 3 distinct lines. The electron can go 3→2→1 or 3→1 directly.
Characteristic X-ray intensity depends on the number of inner-shell electrons available (atomic number) and the number of incident electrons (beam current).
E = Δm·c² = 0.1 × 931 MeV ≈ 93 MeV. (Note: typical U-235 fission releases ~200 MeV total, distributed among products).
Δx·Δp ≥ h/(4π). Δp ≥ 1.055×10⁻³⁴/(4π×10⁻¹⁰) ≈ 5.27 × 10⁻²⁵ kg·m/s.
Work function W = hf₀ = 6.63 × 10⁻³⁴ × 6 × 10¹⁴ = 3.98 × 10⁻¹⁹ J ≈ 2.48 eV.
In beta-plus decay, Z decreases by 1, A remains constant. ⁶⁰₂₇Co → ⁶⁰₂₆Ni + e⁺ + νₑ.
