If the velocity of the electron in first in first of `H` atom is `2.18xx10^(6) m//s`, what is its value in third orbit?

Explanation

To find the velocity of the electron in the third orbit of a hydrogen atom, we can use the formula for the velocity of an electron in a hydrogen atom's orbit:

\[ v_n = v_1 \times \frac{Z}{n} \]

Where:
- \( v_n \) is the velocity of the electron in the nth orbit.
- \( v_1 \) is the velocity of the electron in the first orbit.
- \( Z \) is the atomic number of the element (for hydrogen, \( Z = 1 \)).
- \( n \) is the principal quantum number (the orbit number).

### Step-by-Step Solution:

1. **Identify Given Values:**
- The velocity of the electron in the first orbit, \( v_1 = 2.18 \times 10^6 \, \text{m/s} \).
- The atomic number of hydrogen, \( Z = 1 \).
- The orbit number for which we need to find the velocity, \( n = 3 \).

2. **Substitute Values into the Formula:**
\[ v_3 = v_1 \times \frac{Z}{n} \]
\[ v_3 = 2.18 \times 10^6 \, \text{m/s} \times \frac{1}{3} \]

3. **Calculate the Velocity:**
\[ v_3 = 2.18 \times 10^6 \, \text{m/s} \times 0.3333 \]
\[ v_3 = 7.27 \times 10^5 \, \text{m/s} \]

4. **Final Answer:**
The velocity of the electron in the third orbit of the hydrogen atom is:
\[ v_3 = 7.27 \times 10^5 \, \text{m/s} \]

### Summary:
The velocity of the electron in the third orbit of a hydrogen atom is \( 7.27 \times 10^5 \, \text{m/s} \).