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Question

# The kinetic energy of an electron in the 2nd orbit of bohr's model of a hydrogen atom is: (a0 is Bohr radius)

A
h24π2ma20
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B
h216π2ma20
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C
h232π2ma20
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D
h264π2ma20
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Solution

## The correct option is C h232π2ma20The nuclear attraction on the electron = Centrifugal forceSo,kZe2r2=mv2rv2=kZe2mr ...(i)Angular momentum, mvr=nh2π v2=n2h24π2m2r2 ...(ii)Comparing (i) and (ii)kZe2mr=n2h24π2m2r2r=n2Z[h24π2mke2]=n2a0Z∴ vn=hZ2πa0nKE=12mv2n=h2Z28π2ma20n2KE(for n=2,Z=1)=h232π2ma20.Hence, the correct option is C

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