Types of Radioactive Decay放射性衰变的类型

Big Idea · Structure and Properties (SAP)AP Science Practice 1 · Models and Representations~35 min

Learning goals

  • Write nuclides, alpha particles, beta particles, and positrons in ᴬ_Z X notation
  • Describe how the nucleus changes in alpha, beta-minus, beta-plus, and gamma decay, and compare how far each kind of radiation penetrates
  • Write and balance nuclear decay equations using conservation of mass number and atomic number

Before you start

  • Atomic number and mass number (1.3.3)
  • Isotopes (1.3.4)

Nuclei that change on their own

Optional · not on the AP exam: all four lessons in this chapter are optional. The AP Chemistry exam does not cover nuclear or organic chemistry. US Honors chemistry courses usually include this chapter; Chinese high schools teach the nuclear part in physics rather than chemistry.

Every chemical reaction so far has involved only the electrons: the nucleus never changed, so neither did the element. In 1896 Henri Becquerel found that uranium salts give off invisible radiation, and Marie and Pierre Curie went on to discover polonium and radium. Some nuclei are unstable: they spontaneously give off radiation and turn into a different nucleus, changing the element. This is radioactive decay放射性衰变. Carbon-14, mentioned in lesson 1.3.4, is a radioactive isotope.

Nuclear notation

As lesson 1.3.3 showed, a nucleus is made of protons and neutrons. In nuclear chemistry, the mass number A is written at the top left of the symbol and the atomic number (number of protons) Z at the bottom left:

X92238X2922238U,X614X26214C\ce{^{238}_{92}U}, \quad \ce{^{14}_{6}C}

These are also written uranium-238 and carbon-14. The particles involved in decay use the same notation:

ParticleSymbolMass numberCharge
alpha particle (helium nucleus)⁴₂He4+2
beta particle (electron)⁰₋₁e0−1
positron⁰₊₁e0+1
neutron¹₀n10
gamma ray (photon)γ00

Four kinds of decay

  • Alpha decayα 衰变: the nucleus emits an alpha particle. The mass number drops by 4 and the atomic number by 2. Heavy nuclei such as uranium, radium, and radon often decay this way.
  • Beta-minus decayβ⁻ 衰变: a neutron in the nucleus turns into a proton and an electron is emitted. The mass number stays the same and the atomic number rises by 1. Nuclei with too many neutrons, like carbon-14, often decay this way.
  • Positron emissionβ⁺ 衰变 (beta-plus decay): a proton turns into a neutron and a positron is emitted. The mass number stays the same and the atomic number drops by 1. Nuclei with too many protons, like fluorine-18, can decay this way.
  • Gamma emissionγ 衰变: an excited nucleus gives off a gamma ray. Neither the mass number nor the atomic number changes. Gamma rays often accompany other kinds of decay.

The radiations differ greatly in how far they penetrate: a sheet of paper stops alpha particles, a few millimeters of aluminum stops beta particles, and gamma rays take thick lead or concrete to weaken substantially.

Nuclear equations

In a nuclear equation, the mass numbers add up to the same total on both sides, and so do the atomic numbers. For example:

X92238X2922238U→X90234X2902234Th+X24X2224HeX614X26214C→X714X27214N+X−10X2−120e\begin{aligned} &\ce{^{238}_{92}U -> ^{234}_{90}Th + ^{4}_{2}He} \\ &\ce{^{14}_{6}C -> ^{14}_{7}N + ^{0}_{-1}e} \end{aligned}

Check the first: mass number 238 = 234 + 4, atomic number 92 = 90 + 2. Because the atomic number changed, the element changed: uranium became thorium.

Pick a radioactive nuclide below. Fill in the mass number and atomic number of the daughter for its actual decay mode, then see how it moves on a neutron–proton chart:

Try it: write the nuclear decay equation

Uses of radioactivity

  • Americium-241 emits alpha particles and is used in smoke detectors.
  • Fluorine-18 emits positrons and is used in PET scans.
  • Technetium-99m gives off almost nothing but gamma rays and has a half-life of about 6 hours, making it the most widely used isotope for medical imaging.
  • Gamma rays from cobalt-60 are used in radiation therapy and food irradiation.

How Chinese textbooks differ

  • In China, decay, half-life, and nuclear energy are taught in high school physics; the chemistry course only mentions isotopes and radioactivity.
  • The notation is the same: Chinese physics textbooks also write the beta particle as ⁰₋₁e. US textbooks sometimes write it as ⁰₋₁β, and the alpha particle as ⁴₂α.
  • US textbooks may also cover electron capture, where the nucleus pulls in an inner electron, which combines with a proton to make a neutron. The effect on the nucleus is the same as positron emission.

Example 1: the first two steps of the uranium-238 decay chain

Uranium-238 undergoes alpha decay, and the nucleus it forms then undergoes beta-minus decay. Write both nuclear equations.

Step-by-step solution

  1. The patterns. Alpha decay emits ⁴₂He, so the mass number drops by 4 and the atomic number by 2. In beta-minus decay a neutron in the nucleus becomes a proton and an electron, ⁰₋₁e, is emitted: the mass number stays the same and the atomic number goes up by 1.

  2. Alpha decay. Mass number 238 − 4 = 234; atomic number 92 − 2 = 90, which is thorium:

    X92238X2922238U→X90234X2902234Th+X24X2224He\ce{^{238}_{92}U -> ^{234}_{90}Th + ^{4}_{2}He}

  3. Beta-minus decay. The mass number stays 234; the atomic number becomes 90 + 1 = 91, protactinium:

    X90234X2902234Th→X91234X2912234Pa+X−10X2−120e\ce{^{234}_{90}Th -> ^{234}_{91}Pa + ^{0}_{-1}e}

  4. Check. First step: mass number 238 = 234 + 4; atomic number 92 = 90 + 2. Second step: mass number 234 = 234 + 0; atomic number 90 = 91 + (−1). Both are conserved.

  5. A common mistake. Thinking that emitting a negative electron lowers the atomic number by 1. It’s the reverse: the right side gains a −1, so the new nucleus must go up by 1 to keep the totals equal.

Example 2: identifying the missing particle

Find X in each equation and name the kind of decay: (a) ¹⁴₆C → ¹⁴₇N + X; (b) ¹⁸₉F → ¹⁸₈O + X.

Step-by-step solution

  1. The method. Give X a mass number A and an atomic number Z, then use conservation of each to set up an equation.

  2. (a) Find A and Z.

    14=14+A,A=06=7+Z,Z=−1\begin{aligned} 14 &= 14 + A, & A &= 0 \\ 6 &= 7 + Z, & Z &= -1 \end{aligned}

    X is ⁰₋₁e, a beta particle (electron): beta-minus decay.

  3. (b) Find A and Z.

    18=18+A,A=09=8+Z,Z=+1\begin{aligned} 18 &= 18 + A, & A &= 0 \\ 9 &= 8 + Z, & Z &= +1 \end{aligned}

    X is ⁰₊₁e, a positron: positron emission.

  4. Think about it. In beta-minus decay a neutron becomes a proton, so Z goes up by 1 (C → N). In positron emission a proton becomes a neutron, so Z goes down by 1 (F → O). The mass number doesn’t change in either.

  5. Check. Put X back in: (a) 14 = 14 + 0 and 6 = 7 + (−1); (b) 18 = 18 + 0 and 9 = 8 + 1. Both are conserved.

Practice: which kind of decay is it?
  1. ²²⁶Ra → ²²²Rn
  2. ¹³¹I → ¹³¹Xe
  3. ²²Na → ²²Ne
  4. ⁹⁹ᵐTc → ⁹⁹Tc
  5. ⁶⁰Co → ⁶⁰Ni
  6. Mass number down 4, atomic number down 2
  7. A neutron in the nucleus becomes a proton
  8. A proton in the nucleus becomes a neutron
  9. Only energy is released; the element doesn’t change

Common mistakes

Mistake 1: “A beta particle is an electron from outside the nucleus.” It comes from the nucleus: it is emitted when a neutron turns into a proton. That’s why the atomic number rises by 1 and the element changes.

Mistake 2: “Turning a radioactive element into a compound gets rid of its radioactivity.” Chemical reactions involve only the electrons and leave the nucleus alone. Radium is just as radioactive in RaCl₂ as it is as the metal.

Mistake 3: “As in chemical reactions, the elements stay the same.” Nuclear reactions change the nucleus; when the atomic number changes, so does the element. What is conserved is the total mass number and the total atomic number.

Quick check

What nucleus forms when ²³⁸₉₂U emits an alpha particle?

Which kind of radiation penetrates matter the most?

Summary

  • Unstable nuclei spontaneously emit radiation and become different nuclei: radioactive decay. A nuclide is written ᴬ_Z X.
  • Alpha: A − 4, Z − 2. Beta-minus: A unchanged, Z + 1. Positron emission: A unchanged, Z − 1. Gamma: no change in A or Z. Penetrating power: gamma > beta > alpha.
  • In a nuclear equation, the mass numbers balance and so do the atomic numbers.
On to AP (for later)

Nuclear chemistry isn’t in the AP Chemistry Course and Exam Description, so the exam won’t ask for decay equations. The ᴬ_Z X notation, mass numbers, and isotopes do come back in AP topic 1.2 (mass spectra and isotopes). US Honors chemistry courses usually expect you to write these equations.

Data sources: decay modes from the IAEA’s LiveChart of Nuclides.

Practice this chapter: 2.14 · Intro to Nuclear and Organic Chemistry · 6 questions

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