Practicing Success
The ground state energy of the electron in the hydrogen atom is -13.6 eV. What will be its velocity around the nucleus? |
1.7 × 106 m/s 3.4 × 107 m/s 2.2 × 106 m/s 3.4 × 105 m/s |
2.2 × 106 m/s |
The electrostatic force of attraction (Fe = mv2/r) between the revolving electrons and the nucleus provides the required centripetal force (Fc = e2/4πε0) to keep the electrons in their orbits, which gives the relation between v and r as r = e2/4πε0mv2 ..............(1) The total energy (E) of the electron is the sum of kinetic energy (mv2/2) and potential energy (-e2/4πε0r) E = mv2/2 + (-e2/4πε0r) Substituting the value of r from the equation....(1) becomes E = -mv2/2 E = -13.6 eV = -13.6 × 1.6 × 10-19 J m = 9.1 × 10-31 kg v = \(\sqrt {-2E/m}\) v = 2.2 × 106 m/s |