Potential energy between a proton and an electron is given by U=Ke23R3, then radius of Bohr's orbit can be given by

AP EAMCET · PHYSICS · Atomic Physics

Potential energy between a proton and an electron is given by $U = \frac{K e^{2}}{3 R^{3}}$ , then radius of Bohr's orbit can be given by

A $\frac{K e^{2} m}{h^{2}}$
B $\frac{6 π^{3} K e^{2} m}{n^{3} h^{2}}$
C $\frac{2 π}{n} \frac{K e^{2} m}{h^{2}}$
D $\frac{4 π^{2} K e^{2} m}{n^{3} h^{2}}$

Verified Solution

Answer & Solution

Correct Answer

(D) $\frac{4 π^{2} K e^{2} m}{n^{3} h^{2}}$

Step-by-step Solution

Detailed explanation

Since electrostatic force is a conservative force, therefore, F=-dUdx ⇒F=-dUdR=Ke2R4 This force provides the necessary centripetal force, FC=mv2R ⇒Ke2R4=mv2R⇒v2=Ke2mR3 Using Bohr quantization of angular momentum theory,…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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