Velocity of an electron in the Iind stationary orbit of hydrogen atom is

Options

A. Equal to velocity of light
B. Equal to `(1)/( 137)` times velocity oflight
C. Equal to velocity of an electron in sixth stationary orbit of `Li^(+2)`
D. Equal to `(1)/(274)` times of the velocity of light

Answer

To find the velocity of an electron in the second stationary orbit of a hydrogen atom, we can use the formula derived from Bohr's model of the hydrogen atom. The formula for the velocity (v) of an electron in a stationary orbit is given by:

\[ v = \frac{2.18 \times 10^6 \cdot Z}{n} \]

where:
- \( Z \) is the atomic number of the atom,
- \( n \) is the principal quantum number (the orbit number).

### Step-by-Step Solution:

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

**Step 2: Substitute the values into the formula.**
- Plugging in the values into the formula:
\[ v = \frac{2.18 \times 10^6 \cdot 1}{2} \]

**Step 3: Calculate the velocity.**
- Performing the calculation:
\[ v = \frac{2.18 \times 10^6}{2} = 1.09 \times 10^6 \, \text{m/s} \]

**Step 4: Conclusion.**
- The velocity of the electron in the second stationary orbit of the hydrogen atom is \( 1.09 \times 10^6 \, \text{m/s} \).