An electron in a hydrogen atom has a total energy of -3.4 eV. If the magnitude of the centripetal force acting on the electron is approximately 5.1 10⁻⁹ N, the radial distance of the electron from the nucleus is : (Take 1 eV = 1.6 10⁻¹⁹ J)

Step-by-step solution

The kinetic energy K of an electron is equal to the magnitude of its total energy E . K = |E| = 3.4 eV Converting this to Joules: K = 3.4 1.6 10⁻¹⁹ J = 5.44 10⁻¹⁹ J The centripetal force F_c is provided by the electrostatic force, and is related to kinetic energy as: F_c = mv^2 r Since K = 1 2 mv^2 , we can write mv^2 = 2K . Substituting this into the force equation gives: F_c = 2K r Rearranging for the radial distance r : r = 2K F_c Substituting the given values: r = 2 5.44 10⁻¹⁹ 5.1 10⁻⁹ r = 10.88 10⁻¹⁹ 5.1 10⁻⁹