Discussion Forum

A dense collection of an equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let N be the number density of free electrons, each of mass m. When the electrons are subjected to an electric field, they are displaced relatively away from the
heavy positive ions. lf the electric field becomes zero, the electrons being to oscillate about the positive ions with a natural! angular frequency ω_p, which is called the plasma frequency. To
sustain the oscillations, a time-varying electric field needs to be applied that has an angular frequency ω, where a part of the energy is absorbed and a part of it is reflected. As $\omega$  approaches $\omega_{p}$,  all the free electrons are set to resonance together and all the energy is reflected. This is the explanation of the high reflectivity of metals

Taking the electronic change as e and the permittivity as $\epsilon_{0}$ , use dimensional analysis to determine the correct expression for $\omega_{p}$

Answer:

Explanation:

 N= number of electrons per unit volume 

 $\therefore$   $[N]=[L^{-3}],[e]=[q]$

 = [It]=[AT]

 $ [\epsilon_{0}]=[M^{-1}L^{-3}T^{4}A^{2}]$

 Substituting the dimensions, we can see that 

$\left[\sqrt{\frac{Ne^{2}}{m\epsilon_{0}}}\right]=[T^{-1}]$

 Angular frequency has also the dimension $[T^{-1}]$ 

$\therefore$ correct option  is (c)