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According to Heisenberg's uncertainty principle, the product of uncertainties in position and velocities for an electron of mass $9.1 \times 10^{-31} \mathrm{~kg}$ is
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The correct answer is:
$5.8 \times 10^{-5} \mathrm{~m}^2 \mathrm{~s}^{-1}$
Given that mass of electron $=9.1 \times 10^{-31} \mathrm{~kg}$
Planck's constant $=6.63 \times 10^{-34} \mathrm{kgm}^2 \mathrm{~s}^{-1}$
By using $\Delta x \times \Delta p=\frac{h}{4 \pi} ; \quad \Delta x \times \Delta v \times m=\frac{h}{4 \pi}$
where: $\Delta x=$ uncertainty in position
$\Delta v=$ uncertainty in velocity
$\Delta x \times \Delta v=\frac{h}{4 \pi \times m}$
$=\frac{6.63 \times 10^{-34}}{4 \times 3.14 \times 9.1 \times 10^{-31}}=5.8 \times 10^{-5} \mathrm{~m}^2 \mathrm{~s}^{-1}$.
Planck's constant $=6.63 \times 10^{-34} \mathrm{kgm}^2 \mathrm{~s}^{-1}$
By using $\Delta x \times \Delta p=\frac{h}{4 \pi} ; \quad \Delta x \times \Delta v \times m=\frac{h}{4 \pi}$
where: $\Delta x=$ uncertainty in position
$\Delta v=$ uncertainty in velocity
$\Delta x \times \Delta v=\frac{h}{4 \pi \times m}$
$=\frac{6.63 \times 10^{-34}}{4 \times 3.14 \times 9.1 \times 10^{-31}}=5.8 \times 10^{-5} \mathrm{~m}^2 \mathrm{~s}^{-1}$.
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