Decay Equations (OCR Gateway GCSE Physics: Combined Science)

• Nuclear radioactive decay equations show the changes in mass and charge of the nuclei in the decay
• Nuclear equations, just like chemical equations, balance:
  • The sum of the mass numbers on the left of each equation should equal the sum on the right
  • The sum of the atomic numbers should also balance on the left and right

• The parent nucleus is the nucleus that decays
  • Subsequently, the daughter nucleus remaining after the decay

Alpha Decay Equation

• In nuclear equations representing alpha decay:
  • The mass number of the daughter nucleus is 4 less than the parent
  • The atomic number of the daughter nucleus is 2 less than the parent

Alpha decay equation

• The following equation shows Polonium-212 undergoing alpha decay
  • It forms Lead-208 and an alpha particle
  • An alpha particle can also be written as a helium nucleus (Symbol He)

The polonium nucleus emits an alpha particle, causing its mass and charge to decrease. This means it changes into a new element

Beta Minus Decay Equation

• In nuclear equations representing beta minus decay:
  • The mass number of the daughter nucleus is the same as the parent
  • The atomic number of the daughter nucleus is 1 more than the parent

Beta-minus decay equation

• The following equation shows carbon-14 undergoing beta decay
• • It forms nitrogen-14 and a beta particle
  • Beta particles are written as an electron in this equation

The carbon nucleus emits a beta particle, causing its charge to increase. This means it changes into a new element, Nitrogen

Gamma Decay Equation

• In nuclear equations representing gamma decay:
  • The mass number of the daughter nucleus is the same as the parent
  • The atomic number of the daughter nucleus is the same as the parent

Gamma decay equation

• Here is an example of Uranium-238 undergoing gamma decay
  • Notice that the mass number and atomic number of the unstable nuclei remains the same during the decay

Although the Uranium nucleus is unchanged in structure, its energy reduces during gamma 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

ANSWER:  D

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 11 protons and 13 neutrons

11 + 13 = 24

• • The mass number of the original nucleus is 24

Step 2: Calculate the new atomic number

• • During beta decay a neutron changes into a proton and an electron
  • The electron is emitted as a beta particle
  • The neutron has an atomic number of 0 and the proton has an atomic number of 1
  • So the atomic number increases by 1

11 + 1 = 12

• • The new nucleus has an atomic number of 12

Step 3: Calculate the new mass number

• • Protons and neutrons both have a mass number of 1
  • Changing a neutron to a proton will not affect the mass number
  • The new nucleus has a mass number of 24 (the same as before)