When the atomic electron is at infinite distance from the nucleus, its energy is

Options

A. zero
B. positive
C. negative
D. any value

Answer

To determine the energy of an atomic electron when it is at an infinite distance from the nucleus, we can follow these steps:

### Step 1: Understand the Energy Formula
The energy of an electron in a hydrogen-like atom is given by the formula:
\[ E_n = -\frac{13.6 \, Z^2}{n^2} \, \text{eV} \]
where:
- \(E_n\) is the energy of the electron in the nth orbit,
- \(Z\) is the atomic number,
- \(n\) is the principal quantum number (the orbit number).

### Step 2: Consider the Infinite Distance
When the electron is at an infinite distance from the nucleus, we consider the limit where \(n\) approaches infinity:
\[ n \to \infty \]

### Step 3: Substitute \(n\) into the Energy Formula
Substituting \(n = \infty\) into the energy formula:
\[ E_n = -\frac{13.6 \, Z^2}{\infty^2} \]
Since \(\infty^2\) is still \(\infty\), we can simplify this to:
\[ E_n = -\frac{13.6 \, Z^2}{\infty} = 0 \]

### Step 4: Conclusion
Thus, when the atomic electron is at an infinite distance from the nucleus, its energy approaches:
\[ E = 0 \, \text{eV} \]

### Final Answer
The energy of the atomic electron at infinite distance from the nucleus is **zero**.

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