The speed of an electron in the `4^"th"` orbit of hydrogen atom is

Options

A. c
B. `c/137`
C. `c/2192`
D. `c/548`

Answer

To find the speed of an electron in the 4th orbit of a hydrogen atom, we can use the formula for the speed of an electron in a given orbit:

### Step-by-Step Solution:

1. **Identify the Formula**: The speed \( V \) of an electron in the nth orbit of a hydrogen atom is given by the formula:
\[ V = \frac{C}{137} \cdot \frac{Z}{n} \]
where:
- \( C \) is the speed of light,
- \( Z \) is the atomic number,
- \( n \) is the principal quantum number (the orbit number).

2. **Substitute Values**: For hydrogen:
- The atomic number \( Z = 1 \) (since hydrogen has one proton),
- The principal quantum number for the 4th orbit \( n = 4 \).

Substituting these values into the formula:
\[ V = \frac{C}{137} \cdot \frac{1}{4} \]

3. **Simplify the Expression**: Now, we can simplify the expression:
\[ V = \frac{C}{137 \cdot 4} = \frac{C}{548} \]

4. **Conclusion**: Therefore, the speed of the electron in the 4th orbit of a hydrogen atom is:
\[ V = \frac{C}{548} \]

### Final Answer:
The speed of an electron in the 4th orbit of a hydrogen atom is \( \frac{C}{548} \).

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