In the Bohr model of the hydrogen atom, an electron orbits a proton in a circular orbit of radius 0.53 X 10^-10 m. What is electric potential at the electron's orbit due to the proton? What is the Potential Energy of the electron? What is the total energy of the electron in its orbit? What is the ionization energy? Express your results in electron volts.

a) 27.2 V

b) 27.2 V

Explanation:

Charge of the electron = charge of the proton = q = 1.6 * 10⁻¹⁹ C

Radius = r = 0.53*10⁻¹⁰ m

Electric Potential = V = k q/r

k = 9 * 10⁹ N m²/C² = Coulomb's constant.

V = (9 * 10⁹) (1.6 * 10⁻¹⁹) / (0.53*10⁻¹⁰) = 27.2 V

b) Potential Energy of the electron = k q * q / r

= [ (9 * 10⁹) (1.6 * 10⁻¹⁹) (1.6 * 10⁻¹⁹) / (0.53*10⁻¹⁰) ] / (1.6 * 10⁻¹⁹) eV,

since 1 electron volt = (1.6 * 10⁻¹⁹) joules

= 27.2 eV