Question

The ratio of radii of the first three Bohr orbits is:

• A. \( 1 : 1 : 1 \)
• B. \( 1 : 2 : 3 \)
• C. \( 1 : 4 : 9 \)
• D. \( 1 : 8 : 27 \)

Hint:

The radii of Bohr's orbits increase with the square of the principal quantum number \( n \).

Answer 1

The Correct Option is C

Step 1: According to the Bohr model of the atom, the radius of the \( n \)-th orbit is given by: \[ r_n = n^2 \cdot r_1, \] where \( r_1 \) is the radius of the first orbit.
Step 2: The ratio of the radii of the first three orbits is: \[ \frac{r_1}{r_1} : \frac{r_2}{r_1} : \frac{r_3}{r_1} = 1 : 4 : 9. \]
Final Answer: \[ \boxed{1 : 4 : 9} \]