Beta-Plus Emission

Introduction

Some proton-rich nuclides can change a proton into a neutron and emit a positron. This is beta-plus decay. It is related to beta-minus decay but moves atomic number in the opposite direction: Z falls by one while mass number A stays the same. The emitted positron is not a proton; it is the positively charged antiparticle of the electron.

Core explanation

At an introductory level, write proton → neutron + positron + electron neutrino. A proton and a neutron each contribute one nucleon to A, so A remains constant. The parent loses one proton, so daughter Z = parent Z − 1. Charge is conserved: +1 on the proton side and +1 on the positron side. The positron is commonly written ⁰₊₁e or β⁺. The neutrino has no electric charge and contributes no nucleon count.

For a parent ᴬ ZX, the bookkeeping form is ᴬ ZX → ᴬ Z₋₁Y + ⁰₊₁e + νₑ. The daughter Y is identified by its new proton number Z − 1. This cannot be guessed merely from the fact that the emitted particle has positive charge. For fluorine-18, Z = 9 and A = 18, so beta-plus emission gives oxygen-18 with Z = 8: ¹⁸₉F → ¹⁸₈O + ⁰₊₁e + νₑ. The mass-number sum remains eighteen and the charge-number sum is 9 = 8 + 1.

Compare beta-plus and beta-minus carefully. Beta-minus decay converts a neutron to a proton, emits an electron and an antineutrino, and raises Z by one. Beta-plus decay converts a proton to a neutron, emits a positron and a neutrino, and lowers Z by one. Both leave A unchanged because one nucleon changes identity rather than leaving the nucleus as a nucleon. Their different charged emissions are essential to balancing nuclear equations.

A positron and an electron have equal rest mass and opposite electric charge. When a positron eventually meets an electron in matter, they can annihilate, producing photons. In common positron-emission imaging, two 511-keV gamma photons are often produced in nearly opposite directions after the positron slows and annihilates with an electron. Those photons are useful for detection. They are not the same event as the original beta-plus emission, and the positron may travel a short distance before annihilation, which limits how exactly its origin can be located.

Not every proton-rich nucleus can emit a positron. The decay must have enough available energy to create the positron and satisfy conservation laws. An alternative for some nuclides is electron capture, in which a proton combines with an inner electron and changes to a neutron. Both routes reduce Z by one, but their emitted particles and energy requirements differ. If a problem supplies a particular decay mode, use it rather than inferring beta-plus from proton excess alone.

The word “beta” historically names a class of nuclear emissions. It should not lead you to assign one fixed charge to every beta particle. In equations, the subscript or sign distinguishes β⁻ from β⁺. The neutrino is also not interchangeable with the antineutrino in a complete physical description. In many school balancing questions, neutrinos are omitted from the displayed nuclear equation because they have zero A and zero charge, but a fuller account includes them.

Step-by-step reasoning

1. Confirm that the mode is beta-plus emission, not beta-minus emission or electron capture. 2. Keep the parent's mass number A for the daughter. 3. Subtract one from the parent's atomic number Z and identify the daughter element. 4. Add ⁰₊₁e and νₑ to the products in a fuller equation. 5. Check that mass-number and charge-number sums agree on both sides.

Visual explanation

Draw a proton dot inside a nucleus changing to a neutron dot. Show two outgoing arrows, one labelled β⁺ and the other νₑ. Under the parent write “A, Z”; under the daughter write “A, Z − 1.” Farther away, show the emitted positron meeting an ordinary electron and two photons travelling approximately apart, separating emission from later annihilation.

Real-world analogy

If a team member changes from one role to another, total team size is unchanged while the first role's count falls. This resembles constant A and Z reduced by one. The analogy is limited because beta-plus decay also creates particles, releases energy and depends on quantum probabilities.

Real-world example

Fluorine-18 is used in positron-emission tomography. A molecule labelled with fluorine-18 can be administered as a tracer, and detectors register photon pairs associated with positron annihilation. The tracer's chemical transport and the isotope's nuclear decay are linked in the application but are different processes.

Why?

Why is the emitted positive particle not a proton? A proton has nucleon number one and is much more massive than a positron. The positron has nucleon number zero and the same rest mass magnitude as an electron. If a proton actually left the nucleus, A would fall by one; in beta-plus decay A stays the same because a proton inside becomes a neutron.

Common misconception

“Beta-plus decay adds a proton to the daughter because the emitted particle has positive charge.” The positively charged positron leaves the parent. Inside the nucleus, a proton becomes a neutron, so the daughter has one fewer proton. The outgoing positron balances the charge difference.

Worked example

Sodium-22 has A = 22 and Z = 11 and can undergo beta-plus decay. The daughter keeps A = 22 and has Z = 10, which is neon. Write ²²₁₁Na → ²²₁₀Ne + ⁰₊₁e + νₑ. Check A: 22 = 22 + 0 + 0. Check charge-number entries: 11 = 10 + 1 + 0. The parent has 22 − 11 = 11 neutrons, and the daughter has 22 − 10 = 12; one proton has become a neutron.

Quick check

1. If ¹⁸₉F emits a positron, what are the daughter's mass and atomic numbers? Answer: The daughter has A = 18 and Z = 8, giving oxygen-18.

Exam focus

Write the positron as ⁰₊₁e, keep A unchanged and lower Z by one. Distinguish beta-plus emission from beta-minus emission by the sign and from alpha emission by its unchanged nucleon count.

Advanced insight

Positron emission requires an energy difference large enough to account for creating the positron and the relevant atomic-electron mass bookkeeping. Electron capture can occur for some nuclides where positron emission is not energetically allowed. This explains why identifying a likely mode requires measured nuclear energies rather than only comparing proton and neutron counts.

Summary

Beta-plus decay changes a proton into a neutron and emits a positron and an electron neutrino. A stays constant, Z decreases by one and the daughter becomes the element immediately below the parent in atomic number. Later positron annihilation is a separate event that produces detectable photons.

Practice questions

1. Complete ¹⁸₉F → ? + ⁰₊₁e + νₑ. Answer: The daughter is ¹⁸₈O because A stays eighteen and Z falls from nine to eight. 2. How does beta-plus emission differ from alpha emission in its effect on A and Z? Answer: Beta-plus leaves A unchanged and lowers Z by one; alpha emission lowers A by four and Z by two. 3. Why do positron-emission scanners often detect photons instead of the positron directly? Answer: After slowing, the emitted positron can annihilate with an electron and produce photons that travel out to detectors.