What does the negative electronic energy (negative sign for all values of energy) for hydrogen atom means?

Options

A. The energy of an electron in the atom is lower than the energy of a free electron at rest which is taken as zero.
B. When the electron is free from the influence of nucleus it has a negative value which becomes more negative.
C. When the electron is atteracted by the nucleus the energy is obsorbed which means a negative value.
D. Energy is released by hydrogen atom in ground state.

Answer

To understand what the negative electronic energy for a hydrogen atom means, let's break down the concepts step by step.

### Step 1: Understanding Energy Levels
In quantum mechanics, the energy levels of an electron in an atom are quantized. For a hydrogen atom, the energy levels can be described by the formula:

\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]

where \( n \) is the principal quantum number (n = 1, 2, 3,...).

### Step 2: The Concept of Zero Energy
The energy of a free electron (an electron that is not bound to an atom) is defined as zero. This is the reference point for measuring the energy of electrons in atoms.

### Step 3: Negative Energy Values
The negative sign in the energy values for the hydrogen atom indicates that the energy of the electron is lower than that of a free electron. When the electron is bound to the nucleus, it has less energy (more negative) compared to when it is free.

### Step 4: Energy at Infinity
As the electron moves further away from the nucleus (approaching infinity), the energy approaches zero. At \( n = \infty \), the energy is zero, meaning the electron is no longer influenced by the nucleus and is free.

### Step 5: Implications of Negative Energy
The negative energy values imply that work must be done to remove the electron from the influence of the nucleus (to bring it to a state where its energy is zero). This indicates that the electron is in a bound state.

### Step 6: Conclusion
Thus, the negative electronic energy signifies that the energy of the electron in the hydrogen atom is lower than that of a free electron at rest, confirming that the electron is bound to the nucleus.

### Final Answer
The correct interpretation of the negative electronic energy for a hydrogen atom is that the energy of an electron in the atom is lower than the energy of a free electron at rest, which is taken as zero.