Question

If the radius of the first Bohr orbit is \( r \), then the radius of the second Bohr orbit will be

• A. \( \frac{3}{2} r \)
• B. \( 2r \)
• C. \( 8r \)
• D. \( 4r \)

Hint:

The radius of the \( n \)-th Bohr orbit is proportional to \( n^2 \). Therefore, the radius of the second orbit is four times that of the first orbit.

Answer 1

The Correct Option is B

In Bohr's model of the atom, the radius of the \( n \)-th orbit is given by the formula: \[ r_n = n^2 \cdot r_1 \] where: - \( r_n \) is the radius of the \( n \)-th orbit, - \( r_1 \) is the radius of the first Bohr orbit, - \( n \) is the principal quantum number of the orbit. The radius of the first Bohr orbit is given as \( r_1 = r \). Therefore, the radius of the second Bohr orbit (with \( n = 2 \)) will be: \[ r_2 = 2^2 \cdot r_1 = 4r_1 \] Thus, the radius of the second Bohr orbit is \( 2r \). Therefore, the correct answer is: \[ \text{(2) } 2r \]