   Chapter 29, Problem 71PE

Chapter
Section
Textbook Problem

Derive the approximate form of Heisenberg's uncertainty principle for energy and time, Δ E Δ t ≈ h , using the following arguments: Since the position of a particle is uncertain by Δ x ≈ λ , where λ is the wavelength of the photon used to examine it, there is an uncertainty in the time the photon takes to traverse Δ x . Furthermore, the photon has an energy related to its wavelength, and it can transfer some or all of this energy to the object being examined. Thus the uncertainty in the energy of the object is also related to λ . Find Δ t and Δ E ; then multiply them to give the approximate uncertainty principle.

To determine

To derive:

The approximate from for Heisenberg uncertainty Principle for Energy and Time.

Explanation

Given info:

Position of any particle or electron is given by uncertainty ofΔxλ whereλ is the wavelength of the wave associated with it. There is some uncertainty associated with time as well in which the particle travels distanceΔx . There is some energy associated with the wavelength of the particle which means the uncertainty of energy is related to the wavelength.

Formula used:

ΔxλΔp=h/λΔxΔph

Here, p = momentum of the particle

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