IB DP Physics: HL复习笔记7.1.7 Decay Equations

Decay Equations

Changes in N and Z by Radioactive Decay

  • There are four reasons why a nucleus might become unstable, and these determine which decay mode will occur
    • Decays through beta-minus (β-) emission
    • One of the neutrons in the nucleus changes into a proton and a β- particle (an electron) and antineutrino is released
    • The nucleon number is constant
      • The neutron number (N) decreases by 1
      • The proton number (Z) increases by 1
    • The general decay equation for β- emission is:Too many neutrons

Beta-Minus-Decay

8.3.2-Beta-Minus-Decay-Graph

  • Too many protons
    • Decays through beta-plus (β+) emission or electron capture
    • In beta-plus decay, a proton changes into a neutron and a β+ particle (a positron) and neutrino are released
    • In electron capture, an orbiting electron is taken in by the nucleus and combined with a proton causing the formation of a neutron and neutrino
    • In both types of decay, the nucleon number stays constant
      • The neutron number (N) increases by 1
      • The proton number (Z) decreases by 1
    • The general decay equation for β+ emission is:

Beta-Plus-Decay

    • The equation for electron capture is:

Electron-Capture-1

8.3.2-Beta-Plus-Decay-Graph

  • Too many nucleons
    • Decays through alpha (α) emission
    • An α particle is a helium nucleus
    • The nucleon number decreases by 4 and the proton number decreases by 2
      • The neutron number (N) decreases by 2
      • The proton number (Z) decreases by 2
    • The general decay equation for α emission is:

Alpha-Decay

8.3.2-Alpha-Decay-Graph

  • Too much energy
    • Decays through gamma (γ) emission
    • A gamma particle is a high-energy electromagnetic radiation
    • This usually occurs after a different type of decay, such as alpha or beta decay
    • This is because the nucleus becomes excited and has excess energy
  • In summary, alpha decay, beta decay and electron capture can be represented on an N–Z graph as follows:

8.3.2-NZ-Decay-Graph

Worked Example

A nucleus with 84 protons and 126 neutrons undergoes alpha decay. It forms lead, which has the element symbol Pb.4.2.4-Worked-Example-Alpha-DecayWhich of the isotopes of lead pictured is the correct one formed during the decay?

ANSWER:  A

Step 1: Calculate the mass number of the original nucleus

    • The mass number is equal to the number of protons plus the number of neutrons
    • The original nucleus has 84 protons and 126 neutrons

84 + 126 = 210

    • The mass number of the original nucleus is 210

Step 2: Calculate the new atomic number

    • The alpha particle emitted is made of two protons and two neutrons
    • Protons have an atomic number of 1, and neutrons have an atomic number of 0
    • Removing two protons and two neutrons will reduce the atomic number by 2

84 – 2 = 82

    • The new nucleus has an atomic number of 82

Step 3: Calculate the new mass number

    • Protons and neutrons both have a mass number of 1
    • Removing two protons and two neutrons will reduce the mass number by 4

210 – 4 = 206

    • The new nucleus has a mass number of 206

Worked Example

Plutonium-239 is a radioactive isotope that contains 94 protons and emits α particles to form a radioactive isotope of uranium. This isotope of uranium emits α particles to form an isotope of thorium which is also radioactive.

Write two equations to represent the decay of plutonium-239 and the subsequent decay of uranium.

Step 1: Write down the general equation of alpha decayAlpha-DecayStep 2: Write down the decay equation of plutonium into uraniumPlutonium-Decay-WEStep 3: Write down the decay equation of uranium into thoriumUranium-Decay-WE

Worked Example

WE-Alpha-decay-question-image1_3

ANSWER: C

Alpha-decay-worked-example-2_1Alpha-decay-worked-example-3

Worked Example

A radioactive substance with a nucleon number of 212 and a proton number of 82 decays by β-plus emission into a daughter product which in turn decays by further β-plus emission into a granddaughter product.WE-Beta-emission-question-imageWhich letter in the diagram represents the granddaughter product?

ANSWER: A11.1.9-Worked-example-beta-emission-2

 

 

 

 

 

 

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