Question:
The ratio of radii of the first three Bohr orbits is:
The ratio of radii of the first three Bohr orbits is:
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The radii of Bohr's orbits increase with the square of the principal quantum number \( n \).
Updated On: Jan 12, 2026
- \( 1 : 1 : 1 \)
- \( 1 : 2 : 3 \)
- \( 1 : 4 : 9 \)
- \( 1 : 8 : 27 \)
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The Correct Option is C
Solution and Explanation
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: \[ \boxed{1 : 4 : 9} \]
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: \[ \boxed{1 : 4 : 9} \]
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