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.
Characteristic X-ray intensity depends on the number of inner-shell electrons available (atomic number) and the number of incident electrons (beam current).
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.
Boron-10 and Cadmium have high neutron absorption cross-sections and are used in control rods to regulate chain reactions in nuclear reactors.
A = A₀(1/2)^(t/T₁/₂). 1000 = 8000(1/2)^(20/T₁/₂). (1/8) = (1/2)³, so 20/T₁/₂ = 3, T₁/₂ = 6.67 hours.
In Compton effect, photon transfers energy to electron, losing energy and increasing wavelength. Δλ = (h/m_e c)(1 - cosθ).
λ = h/p = h/√(2mE). For 50 eV electron: λ = 6.63×10⁻³⁴/√(2×9.1×10⁻³¹×50×1.6×10⁻¹⁹) ≈ 0.173 nm.
Using Rydberg formula: 1/λ = R(1/1² - 1/2²) = R(3/4). With R = 1.097 × 10⁷ m⁻¹, λ ≈ 121.6 nm (Lyman alpha line).
