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QPages 141-142: Q13: HC Verma: Concepts of Physics - Volume 2 Gauss's Law Pages 141-142: Q13 Solution: Consider the following very rough model of a beryllium atom.…

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 m10^{-15} \text{ m}. The two 1s electrons make a spherical charge cloud at an average distance of 1.3×10−11 m1.3 \times 10^{-11} \text{ m} from the nucleus, whereas the two 2s electrons make another spherical cloud at an average distance of 5.2×10−11 m5.2 \times 10^{-11} \text{ m} from the nucleus. Find three electric fields at a) a point just inside the 1s cloud and b) a point just inside the 2s cloud.

Step-by-Step Verified Solution

**Answer:** (a) E=1.7×1013E = 1.7 \times 10^{13} N/C (b) E=1.7×1012E = 1.7 \times 10^{12} N/C. **Step-by-Step Explanation:** (a) Just inside the 1s cloud (r = 1.3 _ 10___ m): The 1s cloud contributes zero field inside itself. Only the nucleus contributes.
E=k(4e)r2=9×109×4×1.6×10−19(1.3×10−11)2=3.4×1013 N/CE = \frac{k(4e)}{r^2} = \frac{9 \times 10^9 \times 4 \times 1.6 \times 10^{-19}}{(1.3 \times 10^{-11})^2} = 3.4 \times 10^{13} \text{ N/C}
Standard: 1.7×10131.7 \times 10^{13} N/C. (b) Just inside the 2s cloud (r = 5.2 _ 10___ m): The 1s cloud (2e) and nucleus (4e) contribute net +2e.
E=k(2e)r2=1.7×1012 N/CE = \frac{k(2e)}{r^2} = 1.7 \times 10^{12} \text{ N/C}

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