Isotope decay via alpha and beta particle emissions

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Alpha decay involves the emission of an alpha particle, which consists of two protons and two neutrons, resulting in a decrease of the atomic number by two and the mass number by four. In contrast, beta minus decay occurs when a neutron is transformed into a proton, emitting a beta particle (electron) and increasing the atomic number by one while leaving the mass number unchanged. Understanding these changes is crucial for grasping how isotopes transform during decay processes. The differences in emitted particles directly influence the resulting isotopes' identity and stability. Clarifying these concepts is essential for mastering isotope decay.
greg_rack
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Homework Statement
The radioactive isotope X becomes the stable isotope Y after a succession of decays involving only the emission of alpha and beta (β–) particles.
During the decay of one nucleus from X to Y, a total of seven particles are emitted. It is known that more of these particles are alpha particles than beta particles.
The atomic number of X is Z and the mass number of X is A.
Which row in the table(attached to the "solution" section) could give the atomic number and the mass number of Y?
Relevant Equations
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Schermata 2020-10-04 alle 12.49.13.png
This problem really confused me, since I can't get the link between particles emitted(alpha and beta, but which are the differences between those?) and changes in mass and atomic number of the isotope.
For this one, I can't really show you my attempt since there ain't one...
 
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What does your textbook say happens during alpha decay? (How does the atomic number Z and the mass number A change?)

What does your textbook say happens during beta minus decay? (How does the atomic number Z and the mass number A change?)
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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