Atomic Structure

Step 1: Understanding Beta Decay

Beta-minus ( ) decay occurs when a neutron in the nucleus is converted into a proton while emitting an electron ( particle) and an antineutrino ( ):

This results in the atomic number ( ) of the nucleus increasing by 1, while the mass number ( ) remains unchanged.

Step 2: Definition of Isobars

• Isotopes: Nuclei with the same atomic number ( ) but different mass numbers ( ).
• Isobars: Nuclei with the same mass number ( ) but different atomic numbers ( ).
• Isomers: Nuclei with the same atomic and mass numbers but different energy states.
• Isotones: Nuclei with the same number of neutrons but different atomic numbers.

Since the mass number remains the same during decay but the atomic number changes, the parent and daughter nuclei are isobars.

Step 1: Understanding the Alpha ( ) Decay Contribution
Alpha ( ) decay reduces the atomic number ( ) by 2 and the mass number ( ) by 4 per emitted particle. The given reaction is: Since the mass number decreases from 238 to 206, the total mass loss is: Since each particle reduces by 4, the number of emitted particles is: Step 2: Understanding the Beta ( ) Decay Contribution
Beta-minus ( ) decay increases the atomic number ( ) by 1 without changing the mass number. The total decrease in atomic number is: Each decay reduces by 2, contributing: Since the final change in should be 10, the number of emissions must compensate: Thus, the number of and particles emitted are 6 and 2.