Question

Calculate the uncertainty in the momentum of an electron if it is confined to a linear region of length $1 \times 10^{-10}$ metre.

• A. $5.37 \times 10^{-27} kg\, m \,s ^{-1}$
• B. $5.27 \times 10^{-25} g\, m \,s ^{-1}$
• C. $5.37 \times 10^{-25} g\, m \,s ^{-1}$
• D. $5.27 \times 10^{-25} kg\, m \,s ^{-1}$

Answer 1

Answer: (D)

According to uncertainty principle,

$\Delta x \cdot \Delta p=\frac{h}{4 \pi} \quad$ or $\quad \Delta p=\frac{h}{4 \pi \Delta x}$

$\Delta p=\frac{\left(6.626 \times 10^{-34} kg m ^{2} s ^{-1}\right)}{4 \times 3.14 \times\left(10^{-10} m \right)}=5.27 \times 10^{-25} kg\, m s ^{-1}$