Question

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 1 s electrons make a spherical charge cloud at an average distance of $1.3\times {10}^{-11}m$ form the nucleus, whereas the two 2 s electrons make another spherical cloud at an average distance of $5.2\times {10}^{-11}m$ form the nucleus. Find he electric field at (a) a point just inside the 1 s cloud and (b) a point just inside the 2 s cloud.

Answer 1

(a) Let the three surface be considered as three concentric spheres A, B and C.

Now, charge of ${}^{\prime }{A}^{\prime }=4\times 1.6\times {10}^{-19}C$

charge of ${}^{\prime }{B}^{\prime }=2\times 1.6\times {10}^{-19}C$

charge of ${}^{\prime }{C}^{\prime }=2\times 1.6\times {10}^{-19}C$

As the point 'P' is just inside 1s,

So its distance from the centre $=1.3\times {10}^{-11}m$

Electric field \$\frac{q}{4\pi {\in }_0{x}^2}$

$=\frac{4\times 1.6\times {10}^{-19}}{4\times 3.14\times 8.85\times {10}^{-12}\times (1.3\times {10}^{-11}{)}^2}$

$=3.4\times {10}^{-132}N/C$

(b) For a point just inside the 2s cloud total charge enclosed

$=4\times 1.6\times {10}^{-19}C-2\times 1.6\times {10}^{-19}C$

$=2\times 1.6\times {10}^{-19}C$

Hence, Electricfield

$E=1.065\times {10}^{-12}N/C$

$=1.1\times {10}^{-12}N/C$