Chapter 28, Problem 8Q

To determine

If you knew the position of an object precisely with no uncertainty. How well would your know its momentum?

Answer to Problem 8Q

Solution:

Uncertainty in momentum $=\infty$ i.e. $\Delta P=\infty$

Explanation of Solution

Given data:

Position of an object know precisely $\Delta x=0$

Formula used:

Hessen berg’s principle

$\Delta P.\Delta x>\frac{h}{2\pi }$

h: plank’s constant

$\begin{array}{c}\Delta x=0\\ \Delta P.\Delta x>\frac{h}{2\pi }\\ \Delta P>\frac{h}{2\pi .\left(\Delta x\right)}\\ \Delta P>\frac{h}{2\pi .\left(0\right)}\\ \Delta P=\infty \end{array}$

Hence uncertainty in momentum is very large i.e. $\Delta P=\infty$