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In Bohr's theory of the hydrogen atom, an electron moves in a circular orbit about a proton of radius 0.53 Ao. Speed of electron in Bohr's orbit is about 1N×69× speed of light The value of N is _________.

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answer is 2.

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Detailed Solution

Force on electron causing centripetal acceleration is electrostatic force.∴ mv2r=Ke2r2⇒v=Ke2mr=9×109×1.6×10−1929.1×10−31×0.53×10−10=2.19×106m/s Now, cv=2.99×1082.19×106⇒v=c138⇒v=c2×69m/s Hence, N=2

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In Bohr's theory of the hydrogen atom, an electron moves in a circular orbit about a proton of radius 0.53 Ao. Speed of electron in Bohr's orbit is about 1N×69× speed of light The value of N is _________.