Question

In an atom, an electron is moving with the speed of 660 m/s have an accuracy of 0.005%. The minimum uncertainty with which the position of the electron can be located is:
$(h=6.6\times {10}^{-34}\text{J s};\text{mass of electron},e_m=9\times {10}^{-31}\text{kg and}\pi =3)$

• A. $1.85\times {10}^{-3}\text{m}$
• B. $2.75\times {10}^{-3}\text{m}$
• C. $4.75\times {10}^{-3}\text{m}$
• D. $1.85\times {10}^{-4}\text{m}$

Answer 1

The correct option is A $1.85\times {10}^{-3}\text{m}$

Given:
Speed of electron = 660 m/s
Accuracy of speed = 0.005%
$\text{Uncertainity in speed}\left(\Delta v\right)=660\times \frac{0.005}{100}=0.033\text{m/s}$
Let uncertainity in the position be $\Delta x$.
According to Heisenberg's uncertainty principle:
$m\Delta v\Delta x\ge \frac{h}{4\pi }$
$\therefore \text{Minimum}\Delta x=\frac{h}{4\pi m\Delta v}=\frac{6.6\times {10}^{-34}}{4\times 3\times 9\times {10}^{-31}\times 0.033}=1.85\times {10}^{-3}\text{m}$