- #1

fu11meta1

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## Homework Statement

These questions are out of Modern Physics by Tipler. I feel like I'm close to the answer but missing something small.

#1: A ladybug 5mm in diameter with a mass of 1 mg being viewed through a low power magnifier with a calibrated reticule is observed to be stationary with an uncertainty of 10^-2 mm. How fast might the ladybug actually be walking?

#2 Protons and neutrons in nuclei are bound to the nucleus by exchanging pions ( pi mesons) with each other. This is possible to do without violating energy conservation provided the pion is reabsorbed within a time consistent with the Heisenberg uncertainty relations. Consider the emission reaction p --> p + where m = 135 MeV/c2.

A: Ignoring kinetic energy, by how much is energy conservation violated in this reaction?

B: Within what time interval must the pion be reabsorbed in order to avoid the violation of energy conservation?

## Homework Equations

ΔXΔP ≥ ħ/2

ΔE*τ ≥ ħ

## The Attempt at a Solution

For #1:

I said that since the uncertainty is .01mm the lower boundary(lowest possible measurement for the diameter) is (5 - .01)mm and the upper boundary is (5+.01)mm. so:

ΔP≈ ħ/2(ΔX) (For both X's. You'll get 2 values for P)

Then saying P=MV. so V ≈ ħ/2(M)(ΔX) for both X's.

For #2:

I said that the conservation is violated by the rest energy of one pion. Because p ---> p + π is the reaction.

but I'm not sure what to use for the uncertainty for E (ΔE) in:

τ ≥ ħ/ΔE

My best! Thanks!