Suppose an electron is attracted towards the origin by a force $\frac{k}{r}$ , where, k is a constant and r is the distance of the electron from the origin. By applying Bohr’s model to this system, the radius of the $n^{t h}$ orbital of the electron is found to be $r_{n}$ and the kinetic energy of the electron to be $T_{n}$ . Then, which of the following is true?

Question

Infinity Learn · Accepted Answer

$$1$$. Given Force  $$f=krWe$$ know Centripetal force  $$fc=mv2r$$⇒$$mv2r=kr$$...$$.1$$    $$2$$.  (From$$ Bohr’s $$theory)mvr=nh2$$π....$$.2$$ From $$(1)v=km$$ From $$(2)mkmr=nh2$$π ∴$$r=nh2$$$$π$$mk Kinetic $$energyTn=$$$$KE$$$$=12mv2=12mkm=k2$$ rn∝n  and Tn is independent of n Therefore, the correct answer is $$(B).

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