Question

The ratio of centripetal acceleration for an electron revolving in 3rd and 5th Bohr orbit of hydrogen atom is

• A. \(25:9\)
• B. \(125:27\)
• C. \(625:81\)
• D. \(5:3\)

Hint:

Speed varies as 1/n and radius as n squared, so centripetal acceleration varies as 1/n to the fourth.

Answer 1

The Correct Option is C

Step 1: Use the formulas.
$v_n = \dfrac{v_1}{n}$ and $r_n = n^2 r_1$.

Step 2: Acceleration.
$a_n = \dfrac{v_n^2}{r_n} = \dfrac{v_1^2}{r_1 n^4}$.

Step 3: Ratio.
$\dfrac{a_3}{a_5} = \left(\dfrac{5}{3}\right)^4 = \dfrac{625}{81}$.

Final Answer:
Option (C). \[ \boxed{625 : 81} \]