Question

An atom is placed in an oscillating electric field; the center of charge of the electrons obeys the equation

1000. d2xdt2+mwo2x=qeE                                                                                        

The first term is the electron mass times its acceleration and the second is a restoring force, while the right-hand side is the force from the outside electric field.

a). If the electric field varies with the frequency ω, find the solution of this equation?

b). What is the resonant frequency of this atom?

c). What is the dipole moment p of this atom if the electric field is constant?

d)Let the dipole moment p = a×e_o×E where the constant α is called the polarizability of the atom. It is a measure of how easy it is to induce a moment in an atom with an electric field. What is the formula of α?

e)If there are N atoms in a unit volume, the polarization P - the dipole moment per unit volume - is given by P = N×p. If the electric field E induces an average dipole moment per unit volume P, then κ, the dielectric constant, k-1=PeoE. What is the formula of k?

Answer 1

its times con mass is a side bield e second right hand Electric restoring es the force it the electric ve the outside the o max tmwon = Vet at² The ist term is the electron moss. acceleration and the second es as borce, while the right hand side from the outside Elet Field Varies with the frequency x=VE mcor-62) n Vet moor thy see thery, we that dipole the moment P of a single atom es. P = ve x = Te E m6o The diable moment pes indeed proportional to the Electric field. P-LEot d=ve - 4002 to most moor if there are N atoms in a unit Volume, the Polarization P-the dipde moment per Wnite volume - is given by : P = NP = Natot. K-1 = 2 = NL. K-1 = 4TING2 mwa tot,

let's see eb we can get the right order. of magnituce bor the dirlectric constant of some substance. E- met Wou met for the Electronie Polarizability 22 165 (her K=1+ (2.69 X10' 9 cetoms / cm) (1671) (0.528x100) K=1.00020 - The dislatric hydrogen measured to be Kemp = 1:0026. Khelium a 1.000050 Khelium = 1.000068