The moving bullet of a gun has $10 \ g$ mass and $10^{-5} \ m$ uncertainty in position. Find the uncertainty in velocity.
(N/A) The uncertainty in the position is given by Heisenberg's Uncertainty Principle: $\Delta x \cdot \Delta v \ge \frac{h}{4 \pi \, m}$.
Rearranging for uncertainty in velocity: $\Delta v = \frac{h}{4 \pi \, m \, \Delta x}$.
Given: $h = 6.626 \times 10^{-34} \, J \, s$,$m = 10 \, g = 10^{-2} \, kg$,and $\Delta x = 10^{-5} \, m$.
Substituting the values: $\Delta v = \frac{6.626 \times 10^{-34}}{4 \times 3.1416 \times 10^{-2} \times 10^{-5}}$.
$\Delta v = \frac{6.626 \times 10^{-34}}{1.2566 \times 10^{-6}} = 5.27 \times 10^{-28} \, m \, s^{-1}$.
Rearranging for uncertainty in velocity: $\Delta v = \frac{h}{4 \pi \, m \, \Delta x}$.
Given: $h = 6.626 \times 10^{-34} \, J \, s$,$m = 10 \, g = 10^{-2} \, kg$,and $\Delta x = 10^{-5} \, m$.
Substituting the values: $\Delta v = \frac{6.626 \times 10^{-34}}{4 \times 3.1416 \times 10^{-2} \times 10^{-5}}$.
$\Delta v = \frac{6.626 \times 10^{-34}}{1.2566 \times 10^{-6}} = 5.27 \times 10^{-28} \, m \, s^{-1}$.
Explore More
Similar Questions
In an atom,an electron is moving with a speed of $600 \ m/sec$ with an uncertainty of $0.005\%$. The uncertainty with which the position of the electron can be located is:
Medium
View SolutionThe 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 $h = 6.63 \times 10^{-34} \ J \ s$)
DifficultJEE MAIN 2022
View SolutionProvide the equation for a system where the energy of an atom or molecule does not change with time.
Easy
View SolutionThe uncertainty in the determination of the position of a small ball of mass $10 \ g$ is $10^{-33} \ m$. With what percentage of accuracy can its speed be measured,if it has a speed of $52.5 \ m \ s^{-1}$? (Given: $h = 6.6 \times 10^{-34} \ J \ s$)
DifficultTS EAMCET 2024
View SolutionIf the uncertainty in momentum and uncertainty in the position of a particle are equal,then the uncertainty in its velocity would be given by
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo