Question

An iron ball has a mass of 35 gms and a speed of 50 m/s. If the speed can be measured with in accuracy of 2% then the uncertainty in the position is :

• A. $1.507\times {10}^{-34}m$
• B. $1.507\times {10}^{-31}m$
• C. $1.507\times {10}^{-33}m$
• D. $1.507\times {10}^{-12}m$

Answer 1

The correct option is C $1.507\times {10}^{-33}m$

The uncertainity in speed is 2% or $50\times \frac{2}{100}=1m/s$.

The uncertainity in momentum is $\Delta P=x\Delta V=\frac{35}{1000}\times 1=0.035Kgm/s$.

According to Heisenberg's uncertainity principle :

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

$\Delta x\times 0.035=\frac{6.626\times {10}^{-34}}{4\times 3.1416}$

$\Delta x=1.507\times {10}^{-33}m$

Hence the correct option is C.