Question

The uncertainty in momentum of an electron is $1\times 10^{-5} \,kg \,m/s.$ The uncertainty in its position will be
(Given, $h = 6.62 \times 10^{-34} \,kg\, m^2/s)$

• A. $1.05 \times 10^{-28} m$
• B. $1.05 \times 10^{-26} m$
• C. $5.27 \times 10^{-30} m$
• D. $5.25 \times 10^{-28} m$

Answer 1

Answer: (C)

According to Heisenberg's uncertainty principle
$\Delta p \times \Delta x \geq \frac{h}{4 \pi}$
Uncertainty in momentum
$\Delta p =1 \times 10^{-6} \,kg \,m / s $
$1 \times 10^{-5} \times \Delta x =\frac{6.62 \times 10^{-34}}{4 \times \frac{22}{7}} $
$\Delta x =\frac{6.62 \times 10^{-34} \times 7}{1 \times 10^{-6} \times 4 \times 22} $
$=5.265 \times 10^{-30} \,m$
$ \approx 5.27 \times 10^{-30} \,m$