For an electron the product of velocity of electron and principal quantum no.

Options

A. principal quantum number
B. velocity of the electron
C. energy of the electron
D. frequency of its revolution

Answer

To solve the question regarding the product of the velocity of an electron and its principal quantum number, we can follow these steps:

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

### Step 2: Write the product of velocity and principal quantum number
We need to find the product of the velocity of the electron and the principal quantum number \( n \):
\[ v \times n = \left( \frac{2.18 \times 10^6 \times Z}{n} \right) \times n \]

### Step 3: Simplify the expression
When we simplify the expression:
\[ v \times n = 2.18 \times 10^6 \times Z \]
This shows that the product of the velocity of the electron and the principal quantum number is directly proportional to the atomic number \( Z \) and is independent of \( n \).

### Step 4: Conclusion
Thus, the product of the velocity of the electron and the principal quantum number \( n \) is:
\[ v \times n = 2.18 \times 10^6 \times Z \]
This means that the product is independent of the principal quantum number.

### Final Answer
The product of the velocity of the electron and the principal quantum number is equal to \( 2.18 \times 10^6 \times Z \).

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