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: Understanding the Concept:
In Bohr model the speed of the electron is \(v\propto\dfrac{1}{n}\) and the radius is \(r\propto n^2\).

Step 2: Find the dependence.
\[ a_c = \frac{v^2}{r}\propto\frac{1/n^2}{n^2} = \frac{1}{n^4} \]

Step 3: Take the ratio.
\[ \frac{a_3}{a_5} = \frac{5^4}{3^4} = \frac{625}{81} \]

Step 4: Check the options.
\(25:9\) is \((5/3)^2\), which comes from using \(1/n^2\). \(125:27\) is \((5/3)^3\), which also does not follow. \(5:3\) is the ratio of the principal quantum numbers.

Final Answer:
The ratio is \(625 : 81\), option (C). \[ \boxed{625 : 81} \]