Suppose an electron is attracted towards the origin by a force kr, 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 nth orbital of the electron is found to be rn and the kinetic energy of the electron to be Tn. Then, which of the following is true?
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a
Tn∝1n2,rn∝n2
b
Tn independent of n,rn∝n
c
Tn∝n,rn∝n
d
Tn∝1n,rn∝n2
answer is B.
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Detailed Solution
1. Given Force f=krWe know Centripetal force fc=mv2r⇒mv2r=kr....1 2. (From Bohr’s theory)mvr=nh2π.....2 From (1)v=km From (2)mkmr=nh2π ∴r=nh2πmk Kinetic energyTn=KE=12mv2=12mkm=k2 rn∝n and Tn is independent of n Therefore, the correct answer is (B).