Chapter 39: Problem 17

Does the proposed decay \(n \rightarrow p+\pi^{-}\) violate any conservation rules?

Short Answer

Expert verified

Answer: No, the proposed decay process \(n \rightarrow p + \pi^{-}\) does not violate the conservation of electric charge, baryon number, or lepton number.

Step by step solution

Identify the particles involved in the decay

In the given decay process \(n \rightarrow p + \pi^{-}\), there are three main particles involved: 1. Neutron (n) 2. Proton (p) 3. Pion (π₋)

Examine conservation of electric charge

Let's find the charges of the particles involved in the decay process and then check to see if the total charge is conserved. Initial state: Neutron charge: 0 Final state: Proton charge: +1 (in elementary charge units) Pion charge (π₋): -1 As we can see, the sum of charges in the initial state is equal to the sum of charges in the final state (0 = 1 + (-1)). Therefore, the conservation of electric charge is not violated.

Examine conservation of baryon number

Now, let's find the baryon numbers of the particles involved in the decay process and then check if the total baryon number is conserved. Initial state: Neutron baryon number: +1 Final state: Proton baryon number: +1 Pion baryon number (π₋): 0 As we can see, the sum of baryon numbers in the initial state is equal to the sum of baryon numbers in the final state (+1 = 1 + 0). Therefore, the conservation of baryon number is not violated.

Examine conservation of lepton number

Finally, let's find the lepton numbers of the particles involved in the decay process and then check if the total lepton number is conserved. Initial state: Neutron lepton number: 0 Final state: Proton lepton number: 0 Pion lepton number (π₋): 0 As we can see, the sum of lepton numbers in the initial state is equal to the sum of lepton numbers in the final state (0 = 0 + 0). Therefore, the conservation of lepton number is not violated. #Conclusion# Since the proposed decay process \(n \rightarrow p + \pi^{-}\) does not violate the conservation of electric charge, baryon number, or lepton number, it is a valid decay process according to these conservation rules.

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Does the proposed decay \(n \rightarrow p+\pi^{-}\) violate any conservation rules?

Short Answer

Step by step solution

Identify the particles involved in the decay

Examine conservation of electric charge

Examine conservation of baryon number

Examine conservation of lepton number

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