According to Heisenberg's uncertainty principle, the product of uncertainties in position and velocities for an electron of mass $9 .1 \times 10^{- 31} kg is$

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$2 .8 \times 10^{- 3} m^{2} s^{- 1}$

$3 .8 \times 10^{- 5} m^{2} s^{- 1}$

$5 .8 \times 10^{- 5} m^{2} s^{- 1}$

$6 .8 \times 10^{- 6} m^{2} s^{- 1}$

answer is C.

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Detailed Solution

Given that mass of electron = $9 .1 \times 10^{- 31} kg$

Planck's constant = $6 .63 \times 10^{- 34} m^{2} s^{- 1}$

$\begin{array}{l} By using Δx \times Δp = \frac{h}{4 π} Δx \times Δvm = \frac{h}{4 π} \\ where : Δx = uncertainty in position \\ Δv = uncertainty in velocity \\ Δx \times Δv = \frac{h}{4 π \times m} = \frac{6 .63 \times 10^{- 34}}{4 \times 3 .14 \times 9 .1 \times 10^{- 31}} \\ = 5 .8 \times 10^{- 5} m^{2} s^{- 1} \end{array}$