The radius of an electron orbit in a hydrogen atom is of the order of

Options

A. `10^(-8)m`
B. `10^(-9)m`
C. `10^(-11)m`
D. `10^(-13)m`

Explanation

To find the radius of an electron orbit in a hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Structure of the Hydrogen Atom**:
- A hydrogen atom consists of a nucleus (which contains one proton and no neutrons) and one electron that revolves around the nucleus.

2. **Identify the Formula for the Radius of Electron Orbit**:
- The radius of the electron orbit in a hydrogen atom can be calculated using the formula:
\[ r = r_0 \cdot a^{1/3} \]
- Here, \( r_0 \) is the Bohr radius, and \( a \) is the atomic number of the element (for hydrogen, \( a = 1 \)).

3. **Know the Value of the Bohr Radius**:
- The Bohr radius \( r_0 \) is given as:
\[ r_0 = 0.53 \, \text{Å} = 0.53 \times 10^{-10} \, \text{m} \]

4. **Calculate the Radius for Hydrogen**:
- Since hydrogen has an atomic number of 1, we can substitute \( a = 1 \):
\[ r = r_0 \cdot 1^{1/3} = r_0 \]
- Therefore, the radius of the electron orbit in a hydrogen atom is:
\[ r = 0.53 \times 10^{-10} \, \text{m} \]

5. **Convert the Radius to Standard Form**:
- The radius can also be expressed in scientific notation:
\[ r = 5.3 \times 10^{-11} \, \text{m} \]

6. **Conclusion**:
- The order of the radius of an electron orbit in a hydrogen atom is approximately \( 10^{-10} \, \text{m} \).

### Final Answer:
The radius of an electron orbit in a hydrogen atom is of the order of \( 10^{-10} \, \text{m} \).

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