Question

An atom of gold has 79 protons in its nucleus. Using a purely classical calculation, the innermost electron is found to orbit the nucleus at a distance of 7.8 × 10-13 m. The fundamental charge is 1.6 × 10-19 C, and the mass of the electron is 9.1 × 10-31 kg. For more insight into this situation, see https://www.fourmilab.ch/documents/golden_glow/ a. Using this radius, calculate the electrostatic force between that electron and the nucleus. b. Using that force, calculate the centripetal acceleration of the electron. C. Then calculate the speed that this electron would have. Is it close enough to the speed of light 3. that the Theory of Relativity would have be applied to do it correctly?

Answer 1

olution We know that kąq2 7.8x10-13 = 79q,-798 1.6 x 10-19 C g1.6x10-19 c Then electrostatic force 9x109 x 79x(1.6x10-19 7.8x10-13 F--0.0288N 0.0288 N Centripetal force provided by the electrostatic force ma 0.0288 9.1x10 a 3.163x 1028 m/s2 31 v-3.163x1028 x7.8x10-31 v-3.5x10m/s This value is almost very closer to speed of light so we should apply theory of relativity