Question

What are the differences between beta minus and beta plus decays? Why are they different if they both result in electron capture by a proton or neutron inside the nucleus of an atom?

Answer 1

Beta minus (β-) decay and beta plus (β+) decay are two types of radioactive decay processes that involve the transformation of a nucleon within an atomic nucleus. Although they both involve electron capture by a proton or neutron, there are fundamental differences between the two processes.

1. Beta minus (β-) decay:

   • In β- decay, a neutron inside the nucleus is transformed into a proton, and an electron (β-) and an electron antineutrino (νₑ̄) are emitted.
   • The equation for β- decay is: n → p + e- + νₑ̄
   • The atomic number (Z) of the nucleus increases by 1, while the mass number (A) remains the same.
   • This process occurs when the neutron-to-proton ratio in the nucleus is too high, making the nucleus unstable.

2. Beta plus (β+) decay:

   • In β+ decay, a proton inside the nucleus is transformed into a neutron, and a positron (β+) and an electron neutrino (νₑ) are emitted.
   • The equation for β+ decay is: p → n + e+ + νₑ
   • The atomic number (Z) of the nucleus decreases by 1, while the mass number (A) remains the same.
   • This process occurs when the neutron-to-proton ratio in the nucleus is too low, making the nucleus unstable.

Key differences and reasons for these differences:

1. Charge conservation:

   • In β- decay, the negatively charged electron (β-) is emitted to conserve electric charge. Since the neutron is neutral (charge of 0), it transforms into a proton (charge of +1) to balance the equation.
   • In β+ decay, the positively charged positron (β+) is emitted to conserve electric charge. Since the proton is positively charged (charge of +1), it transforms into a neutron (charge of 0) to balance the equation.

2. Lepton number conservation:

   • In β- decay, the electron antineutrino (νₑ̄) is emitted to conserve lepton number. The lepton number of the electron (e-) is -1, and the lepton number of the electron antineutrino (νₑ̄) is +1, resulting in a total lepton number conservation of 0.
   • In β+ decay, the electron neutrino (νₑ) is emitted to conserve lepton number. The lepton number of the positron (e+) is +1, and the lepton number of the electron neutrino (νₑ) is +1, resulting in a total lepton number conservation of +2.

These differences arise due to the distinct properties and interactions of electrons, positrons, neutrinos, and antineutrinos. The specific decay process that occurs in a given nucleus depends on the initial neutron-to-proton ratio and the stability of the nucleus.