The distance between 3rd and 2nd bohr orbits of hydrogen atom:

Options

A. `0.529xx10^(-8)cm`
B. `2.645xx10^(-8)cm`
C. `2.116xx10^(-8)cm`
D. `1.058xx10^(-8)cm`

Explanation

To find the distance between the 3rd and 2nd Bohr orbits of a hydrogen atom, we can follow these steps:

### Step 1: Understand the formula for the radius of Bohr orbits
The radius of the nth orbit in a hydrogen atom is given by the formula:
\[ R_n = \frac{0.529 \, \text{Å} \cdot n^2}{Z} \]
where:
- \( R_n \) is the radius of the nth orbit,
- \( n \) is the principal quantum number (1, 2, 3, ...),
- \( Z \) is the atomic number (for hydrogen, \( Z = 1 \)).

### Step 2: Calculate the radius of the 3rd orbit (\( R_3 \))
Using the formula for \( n = 3 \):
\[ R_3 = \frac{0.529 \, \text{Å} \cdot 3^2}{1} = \frac{0.529 \, \text{Å} \cdot 9}{1} = 4.761 \, \text{Å} \]

### Step 3: Calculate the radius of the 2nd orbit (\( R_2 \))
Using the formula for \( n = 2 \):
\[ R_2 = \frac{0.529 \, \text{Å} \cdot 2^2}{1} = \frac{0.529 \, \text{Å} \cdot 4}{1} = 2.116 \, \text{Å} \]

### Step 4: Find the distance between the 3rd and 2nd orbits
The distance between the 3rd and 2nd orbits is given by:
\[ \text{Distance} = R_3 - R_2 = 4.761 \, \text{Å} - 2.116 \, \text{Å} = 2.645 \, \text{Å} \]

### Final Answer
The distance between the 3rd and 2nd Bohr orbits of a hydrogen atom is \( 2.645 \, \text{Å} \).

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