Question

Consider an electron moving in the first Bohr orbit of a He\(^+\) ion with velocity \(v_1\). If it is allowed to move in the third Bohr orbit with velocity \(v_3\), determine the correct \(v_3 : v_1\) ratio.\\

• A. 3:1
• B. 2:1
• C. 1:3
• D. 1:2

Answer 1

The Correct Option is C

The velocity of an electron in a Bohr orbit is inversely proportional to the principal quantum number (n):

\( v \propto \frac{1}{n} \)

For the first Bohr orbit (n=1), the velocity is \(v_1\). For the third Bohr orbit (n=3), the velocity is \(v_3\). Using the proportionality:

\( \frac{v_3}{v_1} = \frac{1/3}{1/1} = \frac{1}{3} \)

Thus, the ratio \(v_3 : v_1\) is 1:3.