Question

Estimate the wavelength at which plasma reflection will occur for a metal having the density of electrons $N\approx 4\times {10}^{27}{m}^{-3}$ Take ${ϵ}_0\approx {10}^{-11}$ and $m\approx {10}^{-30}$, where these quantities are in proper SI units.

• A. 800 nm
• B. 600 nm
• C. 300 nm
• D. 200 nm

Answer 1

Answer: (B)

600 nm

${\omega }_p$= $\sqrt{\frac{N{e}^2}{m{e}_0}}$ = $\sqrt{\frac{4\times {10}^{27}\times (1.6\times {10}^{-19}{)}^2}{{10}^{-30}\times {10}^{-11}}}$
${\omega }_p$ = $1.6\times 2\times {10}^{15}$
$f$= $\frac{\omega }{2\pi }$ = $0.5\times {10}^{15}$
$c=fw$
$w$= $\frac{3\times {10}^8}{0.5\times {10}^{15}}$= $600nm$