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Q.66

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 1116

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Short Answer

The muon is a subatomic particle with the same charge as an electron but with a mass that is times greater: Physicists think of muons as "heavy electrons," However, the muon is not a stable particle; it decays with a half-life of into an electron plus two neutrinos. Muons from cosmic rays are sometimes "captured" by the nuclei of the atoms in a solid. A captured muon orbits this nucleus, like an electron, until it decays. Because the muon is often captured into an excited orbit , its presence can be detected by observing the photons emitted in transitions such as and .

Consider a muon captured by a carbon nucleus . Because of its long mass, the muon orbits well inside the electron cloud and is not affected by the electrons. Thus, the muon "sees" the full nuclear charge and acts like the electron in a hydrogen like ion.

a. What is the orbital radius and speed of a muon in the ground state? Note that the mass of a muon differs from the mass of an electron.

b. What is the wavelength of the muon transition?

c. Is the photon emitted in the transition infrared, visible, ultraviolet, or ray?

d. How many orbits will the muon complete during s? Is this a sufficiently large number that the Bohr model "makes sense, " even though the muon is not stable?

(a)

(b)

(c) The photon that is emitted is a-ray photon.

(d)

See the step by step solution

Step by Step Solution

Step:1 Given information

(a)the orbital radius and speed of a muon in the ground state? Note that the mass of a muon differs from the mass of an electron.

Step 2: Calculation

We can begin with an expression for both the radius and muon.

Step 3: Given information

the muon transition?

Step 4: Calculation

We can now use the given equations to express the energy of stationary states:

Step:5 Given information

the transition infrared, visible, ultraviolet, or ray?

Step: 6: Explanation

The photon that is emitted is an x-ray photon.

Step 7: Given information

Is the muon complete during s? Is this a sufficiently large enough number that the Bohr model "makes sense, " even though the muon is not stable?

Step:8 Calculation

(d).The ratio of the muon's half-life to its orbital period can be used. :

This is large number that it makes sense to use the Bohr model

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