Question

The mass of electron is $9.11\times {10}^{-31}$ Kg Planck constant is $6.626\times {10}^{-34}$ Js, the uncertainty involved in the measurement of velocity within a distance of $0.1A^{\circ }$ is:

• A. $5.79\times {10}^{6}m/s$
• B. $5.79\times {10}^{7}m/s$
• C. $5.79\times {10}^{8}m/s$
  
• D. $5.79\times {10}^{5}m/s$
  

Answer 1

The correct option is A

$5.79\times {10}^{6}m/s$

According to Heisenberg uncertainty principle,

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

Now $\Delta p=m\times \Delta v$

Therefore, $\Delta v=\frac{h}{4\pi m\times \Delta x}$

Now substituting the values

$h=6.626\times {10}^{-34}Js$

$m=9.11\times {10}^{-31}kg$

$\Delta x=0.1A^0={10}^{-11}m$

Therefore, $\Delta v=5.79\times {10}^{6}m/s$