Question

The dielectric constant of helium is 1.000684. If N is 2.7 X 10^25 atoms/m^3, what is the radius of the electronic cloud?

(a) 3.78 X 10^-11 m

(b) 4.65 X 10^-11 m

(c) 5.87 X 10^-11 m

(d) 6.12 X 10^-11 m

This question was addressed to me in an international level competition.

My enquiry is from Types of Polarisation topic in chapter Dielectrics of Engineering Physics II

Answer 1

The correct option is (c) 5.87 X 10^-11 m

The best explanation: We know, εo(εr – 1) = Nαe

Or, N4πεor^3 = εo(εr – 1)

r^3 = (εr – 1)/N4π

Here, (εr – 1) = 0.000684, N = 2.7 X 10^25 atoms/m^3, we get

r^3 = 0.000684/4 X 3.14 X 2.7 X 10^25

r = 5.87 X 10^-11 m.