Consider the following very rough model of a beryllium atom. The nucleus has four protons and four neutrons confined to a small volume of radius `10^(-15)m`. The two 1s electrons make a spherical charge cloud at an average distance of `1.3 xx 10^(-11)` m from the nucleus, whereas the two 2s electrons make another spherical cloud at an average distance of `5.2 xx 10^(-11)` m from the nucleus. Find the electric field at (a) a point just inside the 1 s cloud and (b) a point just inside the 2s cloud.

Explanation

(a) Let the three surface be considered as
three concentric spheres A,B and C.
Now, charge of 'A' = 4 xx 1.6 xx (10^-19)C `
` charge of 'B' = 2 xx 1.6 xx (10^-19)C `
` charge of 'C' = 2 xx 1.6 xx (10^-19)C`
As the point 'P' is just inside Is,
So its distance from the centre
`= 1.3 xx (10^-11)m `
Electric field = `q/(4 pi (epsilon_0)x^2)`
` = ((4 xx 1.6 xx (10^-19)/(4 xx 3.14 xx 8.85 xx (10^-12) xx ((1.3 xx (10^-11))^2))`
` = 3.4 xx (10^13)N/C.`
(b) For a point just inside the 2s cloud
total charge enclosed
` = 4 xx 1.6 xx (10^-19)C-2`
` xx 1.6 xx (10^-19)C.`
` = 2 xx 1.6 xx (10^-19)C.`
Hence, Electricfield
`E= 1.065 xx (10^12) N/C `
` = 1.1 xx (10^12)N/C` .