Select the incorrect graph for velocity of `e^(-)` in an orbit vs. Z, `1/n` and n :

Options

A.
B.
C.
D.

Answer

To solve the problem of selecting the incorrect graph for the velocity of an electron (e^(-)) in an orbit versus Z, 1/n, and n, we will follow these steps:

### Step 1: Understand the relationship between velocity, Z, and n
The velocity (V) of an electron in an orbit is given by the formula:
\[ V = 2.18 \times 10^6 \frac{Z}{n} \]
where:
- Z is the atomic number,
- n is the principal quantum number (the orbit number).

### Step 2: Analyze the relationship of V with n
From the formula, we can see that:
\[ V \propto \frac{Z}{n} \]
This means that the velocity is inversely proportional to n. Therefore, if we plot V against n, we would expect to see a hyperbolic relationship.

### Step 3: Analyze the relationship of V with 1/n
Since V is inversely proportional to n, it is directly proportional to 1/n:
\[ V \propto \frac{1}{n} \]
If we plot V against 1/n, we would expect to see a linear relationship (straight line).

### Step 4: Analyze the relationship of V with Z
Since V is directly proportional to Z:
\[ V \propto Z \]
If we plot V against Z, we would also expect to see a linear relationship (straight line).

### Step 5: Evaluate the options
Now, let's evaluate the options based on our analysis:
- **Option A (V vs n)**: This should be a hyperbolic graph. **(Correct)**
- **Option B (V vs 1/n)**: This should be a straight line. **(Correct)**
- **Option C (V vs Z)**: This should also be a straight line. **(Correct)**
- **Option D (V vs n)**: This is incorrectly stated as a straight line, but it should be a hyperbolic graph. **(Incorrect)**

### Conclusion
The incorrect statement is found in **Option D**, where it incorrectly states that the graph of V against n is a straight line, when it should actually be a hyperbola.