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 ×10−11 m from the nucleus, whereas the two 2 s electrons make another spherical cloud at an average distance of 5⋅2 × 10−11 m from the nucleus. Find three electric fields at (a) a point just inside the 1 s cloud and (b) a point just inside the 2 s cloud.

Answer 1

Explanation:

(a) The three electric fields at a point just inside the 1 s cloud: Charge of ‘A’ = $4 \times 1.6 \times$ 10–16 c ; Charge of ‘C’ = $2 \times 1.6 \times$ 10–16c; and ‘B’ has the charge = 2 $\times1.6 \times$10–16 c. Point ‘P’ is just inside 1s. Then, from the center, the distance is 1.3 $\times$ 10–11m.

$=\frac{Q}{4 \pi \varepsilon_{0} x^{2}}=\frac{4 \times 1.6 \times 10^{-19}}{4 \times 3.14 \times 8.85 \times 10^{-12} \times\left(1.3 \times 10^{-11}\right)^{2}}$

= 3.4 × 1013N/C

(b) For the point just inside 2s: charge enclosed totally is 4$\times 1.6 \times$ 10–19 – 2 × 1.6 × 10-19 = 2 × 1.6 × 10–19. So, the electric field is 1.1 $\times$ 1012N/C