An electron in a hydrogen atom is revolving in an orbit at a radial distance of approximately 2.12 10⁻¹⁰ m from the nucleus. The kinetic energy of the electron in this state is approximately : (Take 1 eV = 1.6 10⁻¹⁹ J, e = 1.6 10⁻¹⁹ C and 1 4 ₀ = 9 10⁹ N m ^2 /C ^2 )

Step-by-step solution

The kinetic energy K of an electron in a hydrogen atom is given by the formula: K = 1 4 ₀ e^2 2r Substituting the given values to find the energy in Joules: K = 9 10^9 (1.6 10⁻¹⁹)^2 2 2.12 10⁻¹⁰ K = 9 10^9 2.56 10⁻³⁸ 4.24 10⁻¹⁰ K = 23.04 10⁻²⁹ 4.24 10⁻¹⁰ 5.43 10⁻¹⁹ J To convert this energy into electron-volts (eV), divide by 1.6 10⁻¹⁹ J/eV: K = 5.43 10⁻¹⁹ 1.6 10⁻¹⁹ 3.4 eV Note: The total energy is -3.4 eV, and the potential energy is -6.8 eV. Kinetic energy is always positive and equal in magnitude to the total ene