The graph between the square root of the frequency of a specific line of characteristic spectrum of `X` - rays and the atomic number of the target will be

Options

A.
B.
C.
D.

Explanation

To solve the problem regarding the relationship between the square root of the frequency of a specific line of the characteristic spectrum of X-rays and the atomic number of the target, we can follow these steps:

### Step 1: Understand the Relationship
We start with Moseley's law, which states that the frequency of the X-ray emission lines is related to the atomic number (Z) of the target element. The equation can be expressed as:
\[ \sqrt{\nu} = a(Z - b) \]
where:
- \(\nu\) is the frequency,
- \(Z\) is the atomic number,
- \(a\) and \(b\) are constants.

### Step 2: Rearranging the Equation
From the equation, we can see that:
\[ \sqrt{\nu} = aZ - ab \]
This resembles the equation of a straight line \(y = mx + c\), where:
- \(y\) is \(\sqrt{\nu}\),
- \(x\) is \(Z\),
- \(m\) (the slope) is \(a\),
- \(c\) (the y-intercept) is \(-ab\).

### Step 3: Analyzing the Intercept
The intercept \(-ab\) is a negative quantity, indicating that the graph will not start from the origin. Instead, it will start from a negative value on the y-axis.

### Step 4: Plotting the Graph
To plot the graph:
- The x-axis represents the atomic number \(Z\).
- The y-axis represents \(\sqrt{\nu}\).
- Since the intercept is negative, the line will start below the origin and will slope upwards as \(Z\) increases.

### Step 5: Conclusion
The graph will be a straight line with a negative y-intercept, indicating that as the atomic number increases, the square root of the frequency also increases, but it starts from a negative value on the y-axis.

Thus, the correct answer is that the graph is a straight line with a negative intercept.

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