Radius of Bohr's orbit of hydrogen atom is

Options

A. `0.24 Å`
B. `0.48Å`
C. `0.53Å`
D. `1.06Å`

Answer

To find the radius of Bohr's orbit for a hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula**:
The radius of the nth orbit in a hydrogen atom is given by the formula:
\[ r_n = \frac{0.529 \, n^2}{Z} \]
where:
- \( r_n \) is the radius of the nth orbit,
- \( n \) is the principal quantum number,
- \( Z \) is the atomic number.

2. **Identify the Values**:
For hydrogen:
- The atomic number \( Z = 1 \).
- The principal quantum number for the first orbit \( n = 1 \).

3. **Substitute the Values into the Formula**:
Plugging in the values into the formula:
\[ r_1 = \frac{0.529 \times 1^2}{1} \]

4. **Calculate the Radius**:
Simplifying the equation:
\[ r_1 = \frac{0.529 \times 1}{1} = 0.529 \, \text{angstrom} \]

5. **Round the Result**:
The value \( 0.529 \, \text{angstrom} \) can be rounded to \( 0.53 \, \text{angstrom} \).

6. **Select the Correct Option**:
From the given options:
- Option 1: 0.24 angstrom
- Option 2: 0.48 angstrom
- Option 3: 0.53 angstrom
- Option 4: 1.06 angstrom

The correct answer is **Option 3: 0.53 angstrom**.

### Final Answer:
The radius of Bohr's orbit of the hydrogen atom is **0.53 angstrom**.

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