An electron moves with a speed of $300 \ ms^{-1}$ with an uncertainty of $0.01\%$. Find the uncertainty in its position.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
The uncertainty in position $(\Delta x)$ is calculated using Heisenberg's uncertainty principle: $\Delta x \cdot m \Delta v \geq \frac{h}{4 \pi}$.
Given:
Speed $(v) = 300 \ ms^{-1}$
Uncertainty in speed $(\Delta v) = 0.01\% \text{ of } 300 \ ms^{-1} = \frac{0.01}{100} \times 300 = 3 \times 10^{-2} \ ms^{-1}$.
Mass of electron $(m) = 9.1 \times 10^{-31} \ kg$.
Planck's constant $(h) = 6.626 \times 10^{-34} \ J \ s$.
Substituting the values:
$\Delta x = \frac{h}{4 \pi m \Delta v}$
$\Delta x = \frac{6.626 \times 10^{-34}}{4 \times 3.1416 \times 9.1 \times 10^{-31} \times 3 \times 10^{-2}}$
$\Delta x \approx 1.93 \times 10^{-3} \ m$.

Explore More

Similar Questions

The uncertainty in the velocities of two particles $A$ and $B$ are $0.03 \ m \ s^{-1}$ and $0.01 \ m \ s^{-1}$ respectively. The mass of $B$ is four times the mass of $A$. The ratio of uncertainties in their positions is

If the uncertainty in velocity and position of a minute particle in space are $2.4 \times 10^{-26} \, m \, s^{-1}$ and $10^{-7} \, m$ respectively,the mass of the particle in $g$ is $....$ (Nearest integer).
(Given: $h = 6.626 \times 10^{-34} \, J \, s$)

The minimum uncertainty in the speed of an electron in a one-dimensional region of length $2 a_{0}$ (where $a_{0} = \text{Bohr radius} = 52.9 \ pm$) is $km \ s^{-1}$. (Given: Mass of electron $= 9.1 \times 10^{-31} \ kg$,Planck's constant $h = 6.63 \times 10^{-34} \ J \ s$)

$A$ golf ball of mass $m$ has a speed of $50 \ m \ s^{-1}$. If the speed can be measured within an accuracy of $2 \%$,the uncertainty in the position is

If uncertainty in the measurement of position and momentum of a microscopic object of mass $m$ are equal,then the uncertainty in the measurement of velocity is given by the expression:

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo