An electron is revolving in a circular orbit of a hydrogen atom with a radius of 2.12 10⁻¹⁰ m. The kinetic energy of the electron in this orbit is approximately: [Take 1 4 ₀ = 9 10^9 N m ^2 C ⁻² and charge of electron e = 1.6 10⁻¹⁹ C]

Step-by-step solution

The electrostatic force between the nucleus and the electron provides the necessary centripetal force for the electron to revolve in its orbit. mv^2 r = 1 4 ₀ e^2 r^2 The kinetic energy K of the electron is given by: K = 1 2 mv^2 = 1 4 ₀ e^2 2r Substituting the given values, we get the kinetic energy in Joules: K = 9 10^9 (1.6 10⁻¹⁹)^2 2 2.12 10⁻¹⁰ J To convert the kinetic energy into electron-volts (eV), divide by 1.6 10⁻¹⁹ C: K = 9 10^9 1.6 10⁻¹⁹ 2 2.12 10⁻¹⁰ eV K = 14.4 10⁻¹⁰ 4.24 10⁻¹⁰ eV K 3.4 eV Answer: 3.4 e