   Chapter 29, Problem 63PE

Chapter
Section
Textbook Problem

(a) If the position of a chlorine ion in a membrane is measured to an accuracy of 1.00 μm , what is its minimum uncertainty in velocity, given its mass is 5.860 × 10 − 26 kg? (b) If the ion has this velocity, what is its kinetic energy in eV, and how does this compare with typical molecular binding energies?

To determine

(a)

The minimum uncertainty in the velocity of chlorine ion.

Explanation

Given:

Accuracy of measurement of position,Δx=1μm

Mass of the chlorine ion,m=5.86×1026kg

Formula used:

The expression for the minimum uncertainty in velocity is,

ΔxΔph4π        ...... (1)

The expression for the uncertainty in momentum is,

Δp=mΔv        ...... (2)

Calculation:

Combine equation (1) and equation (2).

Δx(mΔv)=h4πΔv=h4πΔxm

Substitute the given values in above expression to calculate the minimum uncertainty in velocity

To determine

(b)

The kinetic energy of chlorine ion.

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