Question

The ground state energy of hydrogen atom is \(-13.6 \, \text{eV}\). The kinetic and potential energy of the electron in the second excited state is respectively

• A. \( +3.02 \, \text{eV}, -1.51 \, \text{eV} \)
• B. \( +1.51 \, \text{eV}, -3.02 \, \text{eV} \)
• C. \( -1.51 \, \text{eV}, +3.02 \, \text{eV} \)
• D. \( +3.02 \, \text{eV}, +1.51 \, \text{eV} \)

Hint:

In hydrogen atom, total energy is negative; kinetic energy is equal to the magnitude of total energy, while potential energy is twice the total energy.

Answer 1

The Correct Option is B

Step 1: Energy of the second excited state.
Second excited state corresponds to \(n = 3\). Total energy is \[ E_n = \frac{-13.6}{n^2} = \frac{-13.6}{9} = -1.51 \, \text{eV}. \]
Step 2: Relation between kinetic and potential energy.
For an electron in a hydrogen atom, \[ K = -E, \quad U = 2E. \]
Step 3: Calculating kinetic and potential energy.
\[ K = 1.51 \, \text{eV}, \quad U = -3.02 \, \text{eV}. \]
Step 4: Conclusion.
The kinetic energy is \(+1.51 \, \text{eV}\) and the potential energy is \(-3.02 \, \text{eV}\).