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)

Given that mass of electron =$9.1\times10^{-31} \,kg$
Planck’s constant $=9.63\times10^{-34} m^{2} s^{-1}$
By using $\Delta x\Delta p =\frac{h}{4\pi}; \Delta x \times\Delta\nu\times m=\frac{h}{4\pi} $
where: $\Delta x =$ uncertainty in position
$\Delta x =$ uncertainty in position
$\Delta x\times\Delta\nu=\frac{h}{4\pi\times m}=\frac{6.63\times10^{-34}}{4\times3.14\times9.1\times10^{-31}} $
$=5.8 \times10^{-5} m^{2} s^{-1}$