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β⁻ emission is an emission of an electron by converting a neutron to a proton. Hence, in β⁻ decay, the atomic number  of daughter atom increases by 1 than the parent atom and mass number is not changed in the formed daughter nucleus.

Hence, formed daughter atom should have 89 + 1 = 90 as atomic number. Hence, the daughter atom should be Th (Thorium)

The equation is

₈₉²²⁸Ac → ₉₀²²⁸Th + ₋₁⁰β + energy

The balanced nuclear equation for the formation of ₈₉²²⁸Ac through a beta decay is given by;

₈₉²²⁸Ac → ₉₀²²⁸Th + ₋₁⁰e + energy

Further Explanation

Radioactivity

  • Radioactivity refers to the process by which unstable radioactive isotope undergoes spontaneous decay by releasing energy and emitting particles such as alpha, beta or gamma particles.
  • There are three types of decay; alpha decay, beta decay and gamma decay.

Beta decay

  • This is a type of radioactive decay in which an unstable nuclide undergoes decay to emit energy and beta particles.
  • During beta decay, the atomic mass of the decaying atom increases by 11 while the mass number remains the same.
  • Beta particle is equivalent to an electron,₋₁⁰e.

Alpha decay

  • It is a type of radioactive decay in which emission of energy is coupled by the release of alpha particles.
  • When an unstable isotope undergoes alpha decay, its atomic mass decreases by 2 while its mass number decreases by 4.
  • An alpha particle is equivalent to helium nucleus, ₂⁴He.

Gamma decay

  • It is a type of decay that only involve release of energy from an unstable isotope. It occurs normally after a beta decay or alpha decay.
  • When gamma decay occurs, the atomic number and the mass number of the decaying isotope remains the same.

Keywords: Decay, beta decay, alpha decay, gamma decay

Learn more about:

  • Radioactive decay:https://brainly.com/question/10745621
  • Alpha decay: https://brainly.com/question/1898040
  • Beta decay: https://brainly.com/question/2205240
  • Gamma decay: https://brainly.com/question/8739635

Level: High school \

Subject: Physics

Topic: Radioactivity

Sub-topic: Beta decay.

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