Question

In an atom, an electron is moving with the speed of 600 $m/s$ have an accuracy of 0.005%. The minimum uncertainity with which the position of the electron can be located is:
$h=6.6\times {10}^{-34}Js,\text{mass of electron},e_m=9.1\times {10}^{-31}kg$

• A. $5.10\times {10}^{-3}m$
• B. $1.92\times {10}^{-3}m$
• C. $3.84\times {10}^{-3}m$
• D. $1.52\times {10}^{-3}m$

Answer 1

The correct option is B $1.92\times {10}^{-3}m$

Given:
Speed of electron = 600 $m/s$
Accuracy of speed = 0.005%
$\text{Uncertainity in speed}\left(\Delta v\right)=600\times \frac{0.005}{100}=0.03m/s$
Let uncertainity in the position be $\Delta x$.
According to Heisenberg's uncertainity principle:
$m\Delta v\Delta x\ge \frac{h}{4\pi }$
$\therefore \text{Minimum}\Delta x=\frac{h}{4\pi m\Delta v}=\frac{6.6\times {10}^{-34}}{4\times 3.14\times 9.1\times {10}^{-31}\times 0.03}=1.92\times {10}^{-3}m$