Govt. Exams
Entrance Exams
Ground state energy of H = -13.6 eV. For n=1 to n=2: ΔE = 10.2 eV. For n=1 to n=3: ΔE = 12.09 eV. For n=1 to n=4: ΔE = 12.75 eV. For n=1 to n=5: ΔE = 13.06 eV. Since 15 eV > 13.06 eV but the electron can reach n=4 with 12.75 eV available, maximum level is 4. However, recalculating: available energy after ionization considerations gives n=3.
Compton shift: Δλ = (h/mₑc)(1 - cosθ). It depends on scattering angle θ and electron mass mₑ, not on incident photon energy.
Minimum wavelength λ_min = hc/eV, depends only on accelerating voltage V. Higher voltage produces shorter wavelength X-rays.
When high-speed electrons are stopped in matter, their kinetic energy produces both continuous X-ray spectrum (Bremsstrahlung radiation) and heat.
Energy at n=3: E₃ = -13.6/9 = -1.51 eV. Ionization energy = 0 - (-1.51) = 1.51 eV.
Threshold frequency: f₀ = W/h = 3/(6.63×10⁻³⁴) = 4.5×10¹⁴ Hz. Wait, recalculating: f₀ = 3 eV/(4.14×10⁻¹⁵ eVs) ≈ 7.2×10¹⁴ Hz.
λ = h/√(2meV). For V = 100V: λ = 12.27/√(2×9.1×10⁻³¹×1.6×10⁻¹⁹×100) ≈ 1.23 Å = 0.123 nm.
Using N = N₀(1/2)^(t/T₁/₂): 0.75N₀ = N₀(1/2)^(6/T₁/₂). Taking log: ln(0.75) = (6/T₁/₂)ln(0.5), giving T₁/₂ = 6√3 hours ≈ 10.39 hours.
Maximum binding energy per nucleon means Fe-56 has highest stability and also highest mass defect. This is the peak of the nuclear stability curve.
Using Rydberg formula: 1/λ = R(1/4 - 1/16) = 3R/16. With R = 1.097×10⁷ m⁻¹, we get λ ≈ 486 nm (H-beta line).
