COMEDK202510 May 2025Evening ShiftPhysicsAtomic PhysicsActual
What is the frequency ' v ' of the electron in Bohr's first orbit of radius ' r ' of the hydrogen atom?
Options
- Av= e^2 2 ₀ h r
- Bv= e^2 4 ₀ h r
- Cv= e^2 2 ₀ h r^2
- Dv= e^2 4 ₀ h r^2
Correct answer
B. v= e^2 4 ₀ h r
Step-by-step solution
For n=1 , Bohr's quantization gives: mv_ orb r = h 2 ... (1) Electrostatic force provides centripetal force: mv_ orb ^2 r = e^2 4 ₀ r^2 ... (2) Dividing (2) by (1): v_ orb r^2 = e^2 2 4 ₀ r^2 h v_ orb = e^2 2 ₀ h Frequency of revolution: v = v_ orb 2 r = e^2 2 ₀ h 2 r = e^2 4 ₀ hr