Calculate the velocity of an electron in the first Bohr orbit of a hydrogen atom

Explanation

To calculate the velocity of an electron in the first Bohr orbit of a hydrogen atom, we can use the formula given by Bohr's model of the atom. The formula for the velocity (v) of an electron in the nth orbit is:

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

Where:
- \( z \) is the atomic number of the element (for hydrogen, \( z = 1 \))
- \( n \) is the principal quantum number (for the first orbit, \( n = 1 \))

### Step-by-Step Solution:

1. **Identify the values of z and n:**
- For hydrogen, the atomic number \( z = 1 \).
- For the first orbit, the principal quantum number \( n = 1 \).

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

3. **Calculate the velocity:**
\[ v = 2.18 \times 10^6 \text{ m/s} \]

Thus, the velocity of the electron in the first Bohr orbit of a hydrogen atom is \( 2.18 \times 10^6 \) m/s.