The speed of an electron in the innermost orbit of the hydrogen atom (Bohr radius = 52.9 pm, $m_{e} = 9.11 \times 10^{- 31} k g$ ) is

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$2.19 \times 10^{4} m s^{- 1}$

$2.19 \times 10^{6} m s^{- 1}$

$2.19 \times 10^{7} m s^{- 1}$

$2.19 \times 10^{8} m s^{- 1}$

answer is B.

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Detailed Solution

$υ = \frac{2 π}{h} (\frac{e^{2}}{4 π ε_{0}}) = \frac{2 (3.14)}{(6.626 \times 10^{- 34} J s)} [\frac{(1.602 \times 10^{- 19} C}{1.112 \times 10^{- 10} C^{2} N^{- 1} m^{- 2}}] = 2.19 \times 10^{6} m s^{- 1}$

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