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Question:

Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons N ≈ 4 × 10²⁷ m⁻³. Take ε₀ ≈ 10⁻¹¹; 1 and m ≈ 10⁻³⁰, where these quantities are in proper SI units. 300 nm 800 nm 600 nm 200 nm

300 nm

600 nm

800 nm

200 nm

Solution:

ωp = √(Ne²/mε₀) = √(4 × 10²⁷ × (1.6 × 10⁻¹⁹)² / (10⁻³⁰ × 10⁻¹¹))
ωp = 1.6 × 2 × 10¹⁵
f = ω/2π = 0.5 × 10¹⁵
c = fλ
λ = c/f = (3 × 10⁸) / (0.5 × 10¹⁵) = 600nm