Radius of the first Bohr’s orbit of hydrogen atom is

Options

A. `1.06Å`
B. `0.22Å`
C. `0.28Å`
D. `0.53Å`

Explanation

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

### Step 1: Understand the Formula
The formula for the radius of the nth orbit in a hydrogen-like atom is given by:
\[ r_n = \frac{0.53 \, \text{Å} \cdot n^2}{Z} \]
where:
- \( r_n \) is the radius of the nth orbit,
- \( n \) is the principal quantum number (1 for the first orbit),
- \( Z \) is the atomic number (1 for hydrogen).

### Step 2: Substitute Values for Hydrogen
For hydrogen:
- The atomic number \( Z = 1 \),
- The principal quantum number for the first orbit \( n = 1 \).

### Step 3: Calculate the Radius
Substituting the values into the formula:
\[ r_1 = \frac{0.53 \, \text{Å} \cdot 1^2}{1} = 0.53 \, \text{Å} \]

### Step 4: Conclusion
Thus, the radius of the first Bohr's orbit of the hydrogen atom is:
\[ \text{Radius} = 0.53 \, \text{Å} \]

### Final Answer
The radius of the first Bohr’s orbit of the hydrogen atom is **0.53 Å**.

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