Consider a hydrogen atom in the ground state; what is the energy of its electron?

• A. -3.4 eV
• B. 0 eV
• C. -1.51 eV
• D. -13.6 eV

Answer: (D)

Verified step by step guidance

1. Understand that the energy levels of electrons in a hydrogen atom are quantized and can be calculated using the formula: $E=\frac{-RH}{n^2}$, where $RH$ is the Rydberg constant (approximately 13.6 eV) and $n$ is the principal quantum number.
2. Recognize that the ground state of a hydrogen atom corresponds to the principal quantum number $n=1$.
3. Substitute $n=1$ into the energy formula: $E=\frac{-13.6}{1^2}$.
4. Calculate the energy using the formula, which simplifies to $-13.6$ eV for the ground state.
5. Conclude that the energy of the electron in the ground state of a hydrogen atom is $-13.6$ eV, which matches the correct answer provided.