Question

An electron is revolving in its Bohr orbit having Bohr radius of 0.529 Å, then the radius of third orbit is

• A. 4.761 Å
• B. 4234 nm
• C. 5125 nm
• D. 4496 Å

Answer 1

The Correct Option is A

To determine the radius of the nth orbit in the Bohr model, we use the formula:

\( r_n = r_1 \cdot n^2 \) 

Where:

• \( r_n \) is the radius of the nth orbit
• \( r_1 \) is the Bohr radius = \( 0.529 \, \text{Å} \)
• \( n \) is the principal quantum number (orbit number)

For the third orbit (\( n = 3 \)):

\( r_3 = r_1 \cdot 3^2 = 0.529 \, \text{Å} \cdot 9 \)

Calculating the value:

\( r_3 = 4.761 \, \text{Å} \)

Therefore, the radius of the third orbit is: \( \boxed{4.761 \, \text{Å}} \)

Correct Option: (A) 4.761 Å

Answer 2

To find the radius of the nth orbit in the Bohr atomic model, we make use of the following equation:

\( r_n = r_1 \cdot n^2 \)

Explanation of terms: 

• \( r_n \): Radius of the nth energy level
• \( r_1 \): Radius of the first orbit (Bohr radius), which is equal to \( 0.529 \, \text{Å} \)
• \( n \): The principal quantum number or orbit number

Let’s calculate for the third orbit, i.e., when \( n = 3 \):

\( r_3 = r_1 \cdot 3^2 = 0.529 \, \text{Å} \cdot 9 \)

Now, performing the multiplication:

\( r_3 = 4.761 \, \text{Å} \)

Hence, the radius of the third orbit comes out to be: \( \boxed{4.761 \, \text{Å}} \)

Correct Answer: (A) 4.761 Å