Question
The beta minus decay process 13 7 N -> 18 C + B- + -v is proposed in which nitrogen's proton becomes a neutron. The process is not possible because: (1 point)
answers below:
charge conservation is not satisfied
the lepton number is not conserved
the number of protons has changed while the number of neutrons has not
the number of baryons is not conserved
answers below:
charge conservation is not satisfied
the lepton number is not conserved
the number of protons has changed while the number of neutrons has not
the number of baryons is not conserved
Answers
GPT-4o mini
In the proposed beta minus decay process \( ^{13}_{7}N \rightarrow ^{18}_{C} + B^- + \bar{\nu} \), we can analyze the conservation laws:
1. **Charge Conservation**:
- Reactant: Nitrogen \( ^{13}_{7}N \) has a charge of +7.
- Products: Carbon \( ^{18}_{C} \) has a charge of +6 (it has one less proton after the decay), and the emitted beta particle \( B^- \) has a charge of -1. Thus, the total charge is \( +6 - 1 = +5 \).
- Since the initial charge of +7 does not equal the final charge of +5, charge conservation is not satisfied.
2. **Lepton Number Conservation**:
- The emitted beta particle \( B^- \) (which is an electron) carries a lepton number of +1, and the antineutrino \( \bar{\nu} \) also carries a lepton number of +1. Therefore, the total lepton number in the products is +2.
- The initial state has zero lepton number since it is just a nucleon (the nitrogen).
3. **Baryon Number Conservation**:
- The initial nitrogen nucleus is a baryon with a baryon number of +1.
- The carbon nucleus in the products also has a baryon number of +1. The beta particle and antineutrino do not carry baryon number.
- Since baryon number is conserved (+1 in the initial state, +1 in the products), this is satisfied.
4. **Neutron and Proton Counts**:
- In beta decay, a proton converts to a neutron. However, the proposed reaction shows an increase in the total nucleon number (from 13 to 18), which is inconsistent. While the neutron count increases, the proton count does not remain balanced as it should.
Based on this analysis, the correct reason the process is not possible is:
**Charge conservation is not satisfied.**
1. **Charge Conservation**:
- Reactant: Nitrogen \( ^{13}_{7}N \) has a charge of +7.
- Products: Carbon \( ^{18}_{C} \) has a charge of +6 (it has one less proton after the decay), and the emitted beta particle \( B^- \) has a charge of -1. Thus, the total charge is \( +6 - 1 = +5 \).
- Since the initial charge of +7 does not equal the final charge of +5, charge conservation is not satisfied.
2. **Lepton Number Conservation**:
- The emitted beta particle \( B^- \) (which is an electron) carries a lepton number of +1, and the antineutrino \( \bar{\nu} \) also carries a lepton number of +1. Therefore, the total lepton number in the products is +2.
- The initial state has zero lepton number since it is just a nucleon (the nitrogen).
3. **Baryon Number Conservation**:
- The initial nitrogen nucleus is a baryon with a baryon number of +1.
- The carbon nucleus in the products also has a baryon number of +1. The beta particle and antineutrino do not carry baryon number.
- Since baryon number is conserved (+1 in the initial state, +1 in the products), this is satisfied.
4. **Neutron and Proton Counts**:
- In beta decay, a proton converts to a neutron. However, the proposed reaction shows an increase in the total nucleon number (from 13 to 18), which is inconsistent. While the neutron count increases, the proton count does not remain balanced as it should.
Based on this analysis, the correct reason the process is not possible is:
**Charge conservation is not satisfied.**