Question

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:

• A. $ 2.8\times {{10}^{-3}}\,{{m}^{2}}\,{{s}^{-1}} $
• B. $ 3.8\times {{10}^{-5}}\,{{m}^{2}}\,{{s}^{-1}} $
• C. $ 5.8\times {{10}^{-5}}\,{{m}^{2}}\,{{s}^{-1}} $
• D. $ 6.8\times {{10}^{-6}}\,{{m}^{2}}\,{{s}^{-1}} $

Answer 1

Answer: (C)

We will use formula $\Delta x \times \Delta p=\frac{h}{4 \pi}$ to solve problem.
$\Delta x \times \Delta p=\frac{h}{4 \pi} $
$\Delta x \times m \Delta v=\frac{h}{4 \pi} $
$\Delta x \times \Delta v=\frac{h}{4 \pi m} $
$\Delta x=$ uncertainty in position
$\Delta v=$ uncertainty in velocity
$h=$ Planck's constant
$=6.63 \times 10^{-34} \,kg\, m ^{2} \,s ^{-1} $
$m=$ mass of electron
$=9.1 \times 10^{-31} \,kg$
$\therefore {\Delta} x \times \Delta v=\frac{6.63 \times 10^{-34}}{4 \times 3.14 \times 9.1 \times 10^{-31}} $
$=5.8 \times 10^{-5} \,m ^{2} \,s ^{-1}$