The maximum energy is present in any electron at

Options

A. Nucleus
B. Ground state
C. First excited state
D. Infinite distance from the nucleus

Explanation

To determine where the maximum energy is present in any electron, we can analyze the relationship between the energy of an electron and its distance from the nucleus in an atom.

### Step-by-Step Solution:

1. **Understanding Energy Levels**:
The energy of an electron in an atom is quantized and can be described by the formula:
\[ E_n = -\frac{k}{n^2} \]
where \( E_n \) is the energy of the electron in the nth orbit, \( k \) is a constant, and \( n \) is the principal quantum number (the number of the orbit).

2. **Energy and Principal Quantum Number**:
From the formula, we see that as \( n \) increases (i.e., the electron is in a higher energy level), the value of \( E_n \) becomes less negative. This indicates that the energy of the electron is increasing.

3. **Limit of Energy as n Approaches Infinity**:
As \( n \) approaches infinity, the energy \( E_n \) approaches zero:
\[ \lim_{n \to \infty} E_n = 0 \]
This means that at very high values of \( n \), the electron is no longer bound to the nucleus and is essentially free.

4. **Maximum Energy Condition**:
The maximum energy of an electron occurs when it is no longer bound to the nucleus, which happens when \( n \) is infinite. At this point, the electron has the highest energy state, which is zero (the point of being free).

5. **Conclusion**:
Therefore, the maximum energy is present in any electron when it is at an infinite distance from the nucleus.

### Final Answer:
The maximum energy is present in any electron at an infinite distance from the nucleus.

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