Question

A dust particle has mass equal to $ {{10}^{-11}}g, $ diameter $ {{10}^{-4}}cm $ and velocity $ {{10}^{-4}}cm/s. $ The error in measurement of velocity is $ 0.1%. $ What will be the uncertainty in its position?

• A. $ ~0.527\times {{10}^{10}}\text{ }cm $
• B. $ ~5.27\times {{10}^{9}}\text{ }cm $
• C. $ 0.527\times {{10}^{-15}}cm $
• D. $ 0.527\times {{10}^{-9}}cm $

Answer 1

Answer: (D)

$ v={{10}^{-4}}cm\,{{s}^{-1}} $
$ \therefore $ $ \Delta v=\frac{0.1\times {{10}^{-4}}}{100} $
(due to 1% error)
$ =1\times {{10}^{-7}}cm\,{{s}^{-1}} $
Now, $ \Delta v.\Delta x=\frac{h}{4\pi m} $
$ \therefore $ $ \Delta x=\frac{6.626\times {{10}^{-27}}}{4\times 3.14\times {{10}^{-11}}\times {{10}^{-7}}} $
$ =0.527\times {{10}^{-9}}cm $