Energy of electron varies with atomic number as the following curve/line:

Options

A.
B.
C.
D.

Explanation

To solve the question regarding the variation of electron energy with atomic number, we can follow these steps:

### Step 1: Understand the Energy Formula
The energy of an electron in an atom can be expressed using the formula:
\[ E = -\frac{13.6 \, Z^2}{n^2} \]
where:
- \(E\) is the energy of the electron,
- \(Z\) is the atomic number,
- \(n\) is the principal quantum number (energy level).

### Step 2: Identify the Relationship
From the formula, we can see that the energy \(E\) is directly proportional to the square of the atomic number \(Z\) when \(n\) is constant. Thus, we can express this relationship as:
\[ E \propto Z^2 \]

### Step 3: Graphical Representation
Since the energy is proportional to \(Z^2\), if we were to plot a graph of energy \(E\) against \(Z^2\), we would expect a linear relationship. The graph would pass through the origin (0,0) because when \(Z = 0\), \(E\) will also be 0.

### Step 4: Conclusion
Based on the analysis, we can conclude that as the atomic number \(Z\) increases, the energy of the electron also increases proportionally to the square of the atomic number. Therefore, the correct option based on the relationship is that the energy of the electron varies with the atomic number in a way that can be represented by a straight line graph passing through the origin.

### Final Answer
The energy of the electron varies with atomic number \(Z\) as \(E \propto Z^2\), and the graph of energy versus \(Z^2\) will be a straight line passing through the origin.

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