Final answer:
To determine the original number of radioactive atoms of isotope A, multiply the remaining atoms after two half-lives by four, since only one quarter remains. Therefore, if 30 atoms remain, the sample initially had 120 atoms.
Step-by-step explanation:
The question asks how many radioactive atoms of isotope A were present in the original sample if after two half-lives there are 30 atoms remaining. Using the concept of half-life, we can determine the original number. After one half-life, half of the original atoms would remain. After two half-lives, one quarter of the original number of atoms would remain. Thus, if 30 atoms are left after two half-lives, the original sample contained 4 times that amount because 30 is one quarter of the initial amount.
Original amount = 30 atoms × 4 = 120 atoms
Therefore, there were 120 radioactive atoms of isotope A in the original sample.