Answer:

The half-life of a radioactive substance is defined as the time taken for half of the number of nuclei of the substance to decay.

Given that the half-life of A is 2 seconds and the half-life of B is 4 seconds.

Let us assume that the initial number of nuclei of A and B is 100 each.

After 2 seconds:
- Half of the nuclei of A would have decayed
- Half of the nuclei of B would still remain undecayed

Therefore, the number of nuclei of A and B would be 50 and 100 respectively.

After another 2 seconds (i.e., 4 seconds in total):
- Half of the remaining nuclei of A would have decayed (i.e., 25 nuclei would remain)
- Half of the remaining nuclei of B would have decayed (i.e., 50 nuclei would remain)

Therefore, the ratio of remaining nuclei of A to B is 25:50, which can be simplified to 1:2.

Hence, the answer is option (a) 1:2.

Explanation:

To solve this problem, we need to use the concept of half-life of radioactive substances. The half-life of a substance is the time taken for half of the number of nuclei of the substance to decay.

We are given that the half-life of A is 2 seconds and the half-life of B is 4 seconds. This means that after every 2 seconds, the number of nuclei of A would reduce to half its previous value, whereas the number of nuclei of B would reduce to half its previous value after every 4 seconds.

We assume that the initial number of nuclei of A and B is 100 each. After 2 seconds, half of the nuclei of A would have decayed, leaving 50 nuclei. However, since the half-life of B is 4 seconds, half of the nuclei of B would still remain undecayed, leaving 100 nuclei.

After another 2 seconds (i.e., 4 seconds in total), half of the remaining nuclei of A would have decayed, leaving 25 nuclei. On the other hand, since the half-life of B is 4 seconds, half of the remaining nuclei of B would have decayed, leaving 50 nuclei.

Therefore, the ratio of remaining nuclei of A to B is 25:50, which can be simplified to 1:2. Hence, the answer is option (a) 1:2.