Which of the following curves is correct?

Options

A.
B.
C.
D. None of these

Answer

To solve the question regarding which of the given curves is correct based on the relationship between atomic number (z) and frequency (μ), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Variables**:
- The x-axis represents the atomic number (z).
- The y-axis represents the square root of frequency (√μ).

2. **Recall Moseley's Law**:
- Moseley's Law states that the frequency (μ) of the characteristic X-rays emitted by an element is related to its atomic number (z) by the equation:
\[ \sqrt{\mu} = a(z - b) \]
- Here, \(a\) and \(b\) are constants.

3. **Analyze the Equation**:
- Rearranging the equation gives us:
\[ \sqrt{\mu} = az - ab \]
- This can be interpreted as a linear equation in the form of \(y = mx + c\), where:
- \(y = \sqrt{\mu}\)
- \(x = z\)
- \(m = a\) (slope)
- \(c = -ab\) (y-intercept)

4. **Determine the Y-Intercept**:
- The equation indicates that when \(z = b\), \(\sqrt{\mu}\) will be zero. However, since \(z\) cannot be less than \(b\) (as atomic numbers are positive integers), \(\sqrt{\mu}\) will never actually reach zero for any element with a positive atomic number.

5. **Evaluate the Options**:
- **Option 1**: A curve that does not pass through the origin and has a positive y-intercept.
- **Option 2**: A curve that passes through the origin (which is incorrect since \(\sqrt{\mu}\) cannot be zero).
- **Option 3**: A curve that approaches the x-axis but does not touch it.

6. **Conclusion**:
- Since \(\sqrt{\mu}\) cannot be zero for any positive atomic number \(z\), the correct curve must not pass through the x-axis. Therefore, the correct option is **Option 1**.