Question

If hydrogen atom, an electron jumps from bigger orbit to smaller orbit so that radius of smaller orbit is one-fourth of radius of bigger orbit. If speed of electron in bigger orbit was \(v\), then speed in smaller orbit is:

• A. \(v/4\)
• B. \(v/2\)
• C. \(v\)
• D. \(2v\)

Hint:

Smaller orbit means higher speed in Bohr model.

Answer 1

The Correct Option is D

Step 1: In Bohr model: \[ r\propto n^2,\quad v\propto \frac{1}{n} \]
Step 2: If \(r_2=\frac{1}{4}r_1\), then \(n_2=\frac{1}{2}n_1\).
Step 3: \[ v_2=2v_1 \]