Q.

Consider 3rd orbit of He+ (Helium), using non-relativistic approach, the speed of electron in
this orbit will be (take, K = 9 x 109 constant, Z = 2 and Planck's constant, h = 6.6 X 10-34 J-s) [CBSE AIPMT 2015]

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a

3 x 108 ms-1

b

2.92 x 106ms-1

c

1.46 x 106 ms-1

d

0.73 x 106 ms-1

answer is B.

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Detailed Solution

Energy of electron in the 3rd orbit of He+ is

E3=-13.6×Z2n2eV=-13.6×432eV

=-13.6×49×1.6×10-19 J

From Bohr's model, E3=-KE3=-12mv2

  =-13.6×49×1.6×10-19=-12×9.1×10-31×v2

  v2=13.6×4×1.6×10-19×29.1×10-31×9

  v2=212×1012 or v=1.46×106 ms-1

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