The velocity of an electron in the first Bohr orbit of hydrogen atom is `2.19 xx 10^(6)ms^(-1)`. Its velocity in the second orbit would be

Options

A. `1.10 xx10^(6) m sec^(-1)`
B. `4.38 xx 10^(6) m sec^(-1)`
C. `5.50 xx 10^(5) m sec^(-1)`
D. `8.76 xx 10^(6) m sec^(-1)`

Answer

To find the velocity of an electron in the second Bohr orbit of a hydrogen atom, we can use the relationship between the velocities in different orbits.

### Step-by-Step Solution:

1. **Understand the Formula**: The velocity of an electron in the nth orbit (Vn) can be calculated using the formula:
\[ V_n = \frac{V_1}{n} \]
where \( V_1 \) is the velocity in the first orbit and \( n \) is the orbit number.

2. **Identify Given Values**: From the question, we know:
- The velocity in the first orbit \( V_1 = 2.19 \times 10^6 \, \text{m/s} \)
- We want to find the velocity in the second orbit, so \( n = 2 \).

3. **Apply the Formula**: Substitute the known values into the formula:
\[ V_2 = \frac{V_1}{2} = \frac{2.19 \times 10^6 \, \text{m/s}}{2} \]

4. **Calculate the Velocity**: Perform the calculation:
\[ V_2 = 1.095 \times 10^6 \, \text{m/s} \]

5. **Final Result**: Therefore, the velocity of the electron in the second Bohr orbit is:
\[ V_2 \approx 1.10 \times 10^6 \, \text{m/s} \]

### Summary of the Solution:
The velocity of an electron in the second Bohr orbit of a hydrogen atom is approximately \( 1.10 \times 10^6 \, \text{m/s} \).