The speed of the electron in the second orbit in a H-atom is

Options

A. `1.1xx10^(6) m//s`
B. `2.1 xx10^(6) m//s`
C. `1.5xx10^(6) m//s`
D. `2.5xx10^(6) m//s`

Explanation

To find the speed of the electron in the second orbit of a hydrogen atom, we can use Bohr's model of the atom. According to this model, the speed of the electron in the nth orbit is given by the formula:

\[ v_n = 2.188 \times 10^6 \times \frac{Z}{n} \, \text{m/s} \]

Where:
- \( v_n \) is the speed of the electron in the nth orbit,
- \( Z \) is the atomic number of the element,
- \( n \) is the principal quantum number (the orbit number).

### Step-by-Step Solution:

1. **Identify the values for Z and n:**
- For a hydrogen atom, the atomic number \( Z = 1 \).
- We are looking for the speed in the second orbit, so \( n = 2 \).

2. **Substitute the values into the formula:**
\[ v_2 = 2.188 \times 10^6 \times \frac{Z}{n} = 2.188 \times 10^6 \times \frac{1}{2} \]

3. **Calculate the speed:**
\[ v_2 = 2.188 \times 10^6 \times 0.5 = 1.094 \times 10^6 \, \text{m/s} \]

4. **Round the answer:**
- Rounding \( 1.094 \times 10^6 \) gives approximately \( 1.1 \times 10^6 \, \text{m/s} \).

### Final Answer:
The speed of the electron in the second orbit of a hydrogen atom is approximately \( 1.1 \times 10^6 \, \text{m/s} \).