Question

What will be the mass of a particle if uncertainty in its position is ${10}^{-8}$ m and velocity is $5.26\times {10}^{-25}m{s}^{-1}$?

• A. 0.01 kg
• B. 0.1 kg
• C. 1 kg
• D. 10 kg

Answer 1

Answer: (A)

0.01 kg

According to Heisenberg's uncertainty principle:

$\Delta x.\Delta p=\frac{h}{4\pi }$

$\Delta x.\Delta \left(mv\right)=\frac{h}{4\pi }$

$m=\frac{h}{4\pi \Delta x.\Delta v}$

Given: $h=6.626\times {10}^{-34}Js$=Planck's constant

$\Delta x={10}^{-8}$m, $\Delta v=5.26\times {10}^{-25}$ m/s

upon substitution we get:

$m=\frac{6.626\times {10}^{-34}}{4\times 3.14\times {10}^{-8}\times 5.26\times {10}^{-25}}$

$m=0.1\times {10}^{-1}=0.01kg$