Question

In an atom, an electron is moving with a speed of 250 m/s which is measured with an accuracy of 0.001 %. Certainty with which the position of the electron can be located is:
$(h=6.6\times {10}^{-34}kg{m}^2{s}^{-1},\text{Mass of electron}=9.1\times {10}^{-31}kg)$

• A. $3.84\times {10}^{-3}m$
• B. $1.52\times {10}^{-4}m$
• C. $5.1\times {10}^{-3}m$
• D. $2.30\times {10}^{-3}m$

Answer 1

The correct option is D $2.30\times {10}^{-3}m$

Uncertainty in the velocity of the electron = 0.001% of acutal velocity
$\Delta v=\frac{250\times 0.001}{100}=0.025m/s\text{According to Heisenberg's uncertainity principle,}\Delta x.m\Delta v\ge \frac{h}{4\pi }\Delta x=\frac{6.6\times {10}^{-34}}{4\times 3.14\times 9.1\times {10}^{-31}\times 0.025}=2.30\times {10}^{-3}m$