   Chapter 30, Problem 60PE

Chapter
Section
Textbook Problem

Integrated ConceptsParticles called muons exist in cosmic rays and can be created in particle accelerators. Muons are very similar to electrons, having the same charge and spin, but they have a mass 207 times greater. When muons are captured by an atom, they orbit just like an electron but with a smaller radius, since the mass in a B = h 2 4 π 2 m e k q e 2 = 0.529 × 10 − 10   m is 207 m e .(a)Calculate the radius of the n = 1 orbit for a muon in a uranium ion ( Z = 92 ) .(b) Compare this with the 7.5-fm radius of a uranium nucleus. Note that since the muon orbits inside the electron, it falls into a hydrogen-like orbit. Since your answer is less than the radius of the nucleus, you can see that the photons emitted as the muon falls into its lowest orbit can give information about the nucleus.

To determine

(a)

The radius of the n=1 orbit for a muon in an uranium ion (Z=92)

Explanation

Given Data:

Given that particles called muons exists in cosmic rays and can be created in particle accelerators. Muons are very similar to electrons, having same charge and spin, but they have a mass 207 times greater. When muons are captured by an atom, they orbit just like an electron but with a smaller radius, since the mass is aB=h24π2mekqe2=0.529×1010m is 207me

Formula Used:

Radius of the orbit is given as

rn=n2Zaμ

Where rn= Radius of orbit

n= Orbit

Z= Atomic number of an element muon

aμ= Bohr radius of element muon

Bohr Radius of an element muon is given as

aμ=h24π2mμkqμ2

Where h= Planck's constant

mμ= Mass of element muon

k= Coulomb's constant

qμ= Charge on element muon

Calculation:

Given that aμ=0

To determine

(b)

Compare this with the 7.5fm radius of a uranium nucleus.

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