Which of the following is correct for the velocity of electron ?

Options

A.
B.
C.
D. All are correct

Answer

To determine the correct statement regarding the velocity of an electron in an atom, we can follow these steps:

### Step 1: Understand the Expression for Velocity
The velocity of an electron in the nth orbit is given by the formula:
\[ V_n = 2.18 \times 10^6 \times \frac{Z}{n} \, \text{m/s} \]
where:
- \( V_n \) is the velocity of the electron in the nth orbit,
- \( Z \) is the atomic number,
- \( n \) is the principal quantum number.

### Step 2: Analyze the Proportional Relationships
From the expression, we can deduce two key relationships:
1. The velocity \( V_n \) is directly proportional to the atomic number \( Z \):
\[ V_n \propto Z \]
2. The velocity \( V_n \) is inversely proportional to the principal quantum number \( n \):
\[ V_n \propto \frac{1}{n} \]

### Step 3: Evaluate the Graphs
Now, we need to evaluate the graphs provided in the question based on these relationships:
- If \( V_n \) is directly proportional to \( Z \), then as \( Z \) increases, \( V_n \) should also increase.
- If \( V_n \) is inversely proportional to \( n \), then as \( n \) increases, \( V_n \) should decrease.

### Step 4: Identify the Correct Option
Based on the analysis:
- If a graph shows that \( V_n \) increases with increasing \( Z \) and decreases with increasing \( n \), that would be the correct representation of the velocity of an electron in an atom.

Thus, the correct option is the one that reflects these relationships accurately.

### Final Conclusion
The correct option regarding the velocity of the electron is the one that shows:
- Direct proportionality with \( Z \) (as \( Z \) increases, \( V_n \) increases).
- Inverse proportionality with \( n \) (as \( n \) increases, \( V_n \) decreases).