Radius `(r_(n))` of electron in nth orbit versus atomic number (Z) graph is

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Answer

To analyze the relationship between the radius \( r_n \) of an electron in the nth orbit and the atomic number \( Z \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**:
The radius \( r_n \) of an electron in the nth orbit is given by the formula:
\[ r_n = \frac{r_0 n^2}{Z} \]
where \( r_0 \) is a constant, \( n \) is the principal quantum number (orbit number), and \( Z \) is the atomic number.

2. **Identify the Relationship**:
From the formula, we can see that \( r_n \) is inversely proportional to \( Z \). This means that as \( Z \) increases, \( r_n \) decreases, and vice versa.

3. **Behavior at Extremes**:
- When \( Z = 0 \):
If we substitute \( Z = 0 \) into the formula, we find that:
\[ r_n = \frac{r_0 n^2}{0} \rightarrow \infty \]
This indicates that the radius becomes infinitely large when there are no protons (atomic number 0).
- When \( Z \) increases:
As \( Z \) increases, \( r_n \) decreases, approaching zero but never actually reaching it.

4. **Graph Characteristics**:
- The graph of \( r_n \) versus \( Z \) will start from infinity when \( Z = 0 \) and will decrease as \( Z \) increases.
- The curve will approach the horizontal axis (but will never touch it), indicating that \( r_n \) decreases towards zero as \( Z \) becomes very large.

5. **Conclusion**:
Therefore, the correct graph is one that starts from infinity when \( Z = 0 \) and decreases towards zero as \( Z \) increases.