Final answer:
At four half-lives, there would be ⅑⅑⅑⅑ (1/16) of the original uranium isotopes remaining in a rock sample, which means that if we start with N atoms, we would have N/16 atoms left. Thus, if N were 16, the remaining number of isotopes would be 1.
Step-by-step explanation:
At four half-lives, the number of remaining uranium isotopes in a rock sample can be determined by the concept of radioactive decay. After one half-life, half of the original sample remains. After two half-lives, half of that amount remains, and so on. By the fourth half-life, the quantity remaining would be half of the third half-life, which was already one eighth (1/8) of the original sample. Therefore, at four half-lives, the remaining amount would be one sixteenth (1/16) of the original amount of uranium isotopes.
Using powers of 2 for each half-life, since the original amount is 2 to the power of 0 (which is 1), after four half-lives we have:
- First half-life: (1/2)1 = 1/2
- Second half-life: (1/2)2 = 1/4
- Third half-life: (1/2)3 = 1/8
- Fourth half-life: (1/2)4 = 1/16
Thus, if we started with N atoms, after four half-lives, we would have N/16 atoms remaining. If we assume N is 16, then at four half-lives, there would be 1 isotope remaining. So, the correct answer to the student's question would be option (a) 1.