Question

If uncertainty principle is applied to an object of mass 1 microgram, the uncertainty value of velocity and position will be :

• A. $0.2\times {10}^{-4}{m}^2{s}^{-1}$
• B. $0.52\times {10}^6{m}^2{s}^{-1}$
• C. $0.52\times {10}^{-28}{m}^2{s}^{-1}$
• D. $2\times {10}^{-34}{m}^2{s}^{-1}$

Answer 1

The correct option is C $0.52\times {10}^{-28}{m}^2{s}^{-1}$

According to Heisenberg's uncertainity principle:

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

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

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

$m=$mass of object $=1microgram={10}^{-6}$ kg

$\Delta x.\Delta v=\frac{6.626\times {10}^{-34}}{4\pi {10}^{-6}}$

$\Delta x.\Delta v=0.527\times {10}^{-28}{m}^2/s$