Question

In an atom, an electron is moving with a speed of $600m/s$ with an accuracy of $0.005$%. Certainly with which the position of the electron can be located is:

[Given: $h=6.6\times {10}^{-34}kg{m}^2{s}^{-1}$, mass of electron $e_m=9.1\times {10}^{-31}kg$]

• A. $2.15\times {10}^{-3}m$
• B. $2.78\times {10}^{-3}m$
• C. $1.92\times {10}^{-3}m$
• D. $3.24\times {10}^{-3}m$

Answer 1

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

The uncertainity in speed $\Delta v=\frac{0.005}{100}\times 600=0.03m/s$

Certainly with which the position of the electron can be located is:

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

$=\frac{6.6\times {10}^{-34}kg{m}^2{s}^{-1}}{4\times 3.1416\times 9.1\times {10}^{-31}kg\times 0.03m/s}$

$=1.92\times {10}^{-3}m$

Hence, option $C$ is correct.