Question

If the total energy of the electron in the ground state of hydrogen atom is \(-13.6\) eV, then the potential and kinetic energies of an electron in this state respectively are:

• A. \( 27.2 \) eV and \( 13.6 \) eV
• B. \( -13.6 \) eV and \( -27.2 \) eV
• C. \( -27.2 \) eV and \( 13.6 \) eV
• D. \( 27.2 \) eV and \( -13.6 \) eV

Hint:

- The total energy of an electron in an atom is negative, indicating a bound system. - The potential energy is always twice the total energy but negative. - The kinetic energy is the negative of the total energy. - Use the relation \( PE = 2E \) and \( KE = -E \) to find the values.

Answer 1

The Correct Option is C

Step 1: Understanding the Energy Components For a hydrogen atom, the total energy (\(E\)) of an electron in the ground state is given as: \[ E = -13.6 \text{ eV} \] The relation between kinetic energy (\(KE\)), potential energy (\(PE\)), and total energy is: \[ E = KE + PE \] Step 2: Potential Energy Calculation From quantum mechanics, the potential energy of an electron in a hydrogen atom is given by: \[ PE = 2E \] Substituting \(E = -13.6\) eV: \[ PE = 2 \times (-13.6) = -27.2 \text{ eV} \] Step 3: Kinetic Energy Calculation The kinetic energy is related as: \[ KE = -E \] Substituting \(E = -13.6\) eV: \[ KE = 13.6 \text{ eV} \] Thus, the potential and kinetic energies are: \[ PE = -27.2 \text{ eV}, \quad KE = 13.6 \text{ eV} \]