If the speed of the electron in the Bohr's first orbit is x, then speed of the electron in the 3rd orbit would be

Options

A. x/9
B. x/3
C. 3x
D. 9x

Answer

To find the speed of the electron in the third orbit given that the speed in the first orbit is \( x \), we can use Bohr's model of the atom. According to Bohr's theory, the speed of an electron in the nth orbit is given by the formula:

\[ V_n = V_0 \cdot \frac{Z}{n} \]

Where:
- \( V_n \) is the speed of the electron in the nth orbit.
- \( V_0 \) is a constant speed for the first orbit.
- \( Z \) is the atomic number (which we can assume to be 1 for hydrogen).
- \( n \) is the principal quantum number (orbit number).

### Step 1: Determine the speed in the first orbit
From the problem, we know that the speed of the electron in the first orbit (n = 1) is given as \( x \). Thus, we can write:

\[ V_1 = V_0 \cdot \frac{Z}{1} = x \]

### Step 2: Relate \( V_0 \) to \( x \)
From the equation for the first orbit, we can express \( V_0 \) in terms of \( x \):

\[ V_0 \cdot Z = x \]

### Step 3: Calculate the speed in the third orbit
Now, we need to find the speed of the electron in the third orbit (n = 3):

\[ V_3 = V_0 \cdot \frac{Z}{3} \]

### Step 4: Substitute \( V_0 \) in the equation for \( V_3 \)
Using the relationship we found in Step 2, we can substitute \( V_0 \):

\[ V_3 = \frac{x}{Z} \cdot \frac{Z}{3} = \frac{x}{3} \]

### Conclusion
Thus, the speed of the electron in the third orbit is:

\[ V_3 = \frac{x}{3} \]

### Final Answer
The speed of the electron in the third orbit is \( \frac{x}{3} \).

---