Question

2. Consider a simplified model of a triply ionized beryllium-9 atom (Be): four protons plus five neutrons in the atom's nucleus, "orbited" by just one electron at a constant distance of 5.75 x 10m. (Note: This is not the actual distance, but it is the correct order-of-magnitude.) (6 pts.) You can solve (a) & (b) in either order. Label your work clearly a. What is the strength (magnitude) of the attractive electric force between the nucleus and the electron? Show your work. b. What is the magnitude of the electric field at the electron's location? Is its direction toward or away from the nucleus? Show your work.

Answer 1

r = 5.75 times 10^-12 b) Electric field at electron location is E = kq/r^2 E = 9 times 10^9 times 4 times 1.6 times 10^-19/(5.75 times 10^-12)^2 = 1.74 times 10^14 N/C E is directed away from nucleus. a) Force on electron is F = eE E = 1.6 times 10^-19 times 1.74 times 10^14 N F = 2.78 times 10^-5 N c) Gravitational force between Nucleus & electron is F_a = G 9 m_p m_e/r^2 = 6.6 times 10^-11 times 9 times 1.67 times 10^-27 times 9.1 times 10^-31/(5.75 times 10^-12)^2 F_a = 27.3 times 10^-45 N d) F_E/F_a = 0.101 times 10^40