Question

What is the energy of the ground state of a hydrogen atom according to the Bohr model?

• A. \(-13.6\ \text{eV}\)
• B. \(-3.4\ \text{eV}\)
• C. \(-1.51\ \text{eV}\)
• D. \(0\ \text{eV}\)

Hint:

Energy levels of hydrogen follow \[ E_n = -\frac{13.6}{n^2}\ \text{eV} \] The ground state (\(n=1\)) has energy \(-13.6\ \text{eV}\).

Answer 1

The Correct Option is A

Concept: According to the Bohr model, the electron in a hydrogen atom can occupy only certain discrete energy levels. The energy of the \(n^{th}\) orbit is given by \[ E_n = -\frac{13.6}{n^2}\ \text{eV} \] where \(n = 1,2,3,\dots\) is the principal quantum number.
Step 1: Identify the ground state.} The ground state corresponds to the lowest possible energy level, which occurs when \[ n = 1 \]
Step 2: Substitute into the energy formula.} \[ E_1 = -\frac{13.6}{1^2} \] \[ E_1 = -13.6\ \text{eV} \] Thus, the energy of the ground state of hydrogen is \(-13.6\ \text{eV}\).