Question

Find the velocity of an electron in the fourth Bohr orbit of hydrogen atom.

• A. \(2.18\times10^6\,m/s\)
• B. \(5.45\times10^5\,m/s\)
• C. \(1.09\times10^6\,m/s\)
• D. \(4.00\times10^5\,m/s\)

Hint:

In hydrogen atom, \[ v_n=\frac{2.18\times10^6}{n}\;m/s \] Velocity decreases inversely with principal quantum number.

Answer 1

The Correct Option is B

Concept: According to Bohr's model, \[ v_n=\frac{v_1}{n} \] where \[ v_1=2.18\times10^6\,m/s \] for hydrogen atom.

Step 1: Use \(n=4\). \[ v_4=\frac{2.18\times10^6}{4} \] \[ v_4=5.45\times10^5\,m/s \] Final Answer: \[ \boxed{5.45\times10^5\,m/s} \] Hence the correct option is \[ \boxed{(B)} \]