Govt. Exams
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).
Energy of photon E = hf = 4.14 × 10⁻¹⁵ × 6 × 10¹⁵ = 24.84 eV. Maximum KE = E - W = 24.84 - 2 = 22.84 eV (approximately 21.84 eV with standard constants).
First β⁻ decay: ⁹⁴₃₈Sr → ⁹⁴₃₉Y + e⁻ + ν̄. Second β⁻ decay: ⁹⁴₃₉Y → ⁹⁴₄₀Zr + e⁻ + ν̄. Final nucleus is ⁹⁴₄₀Zr.
E = Δm × c². 200 MeV = Δm × 931.5 MeV/amu. Δm = 200/931.5 ≈ 0.215 amu
