Explanation:

The radioactive sample with a half-life of 1 month has an activity of 2 microcurie on 1-8-1991. We need to find its activity two months earlier.

The half-life of a radioactive substance is the time taken for half of the radioactive atoms to decay. Therefore, after one half-life, the activity of the sample will be half of the initial activity.

Calculations:

- The sample has a half-life of 1 month.
- The activity of the sample on 1-8-1991 is 2 microcurie.
- We need to find the activity of the sample two months earlier.
- Let's assume that the activity of the sample two months earlier was A microcurie.
- After one month, the activity of the sample will be 1 microcurie (half of 2 microcurie).
- After two months, the activity of the sample will be 0.5 microcurie (half of 1 microcurie).
- Therefore, the activity of the sample two months earlier was 4 microcurie.

Answer:

The activity of the radioactive sample two months earlier was 4 microcurie.

Reasoning:

The activity of a radioactive substance decreases over time due to the decay of radioactive atoms. The rate of decay is determined by the half-life of the substance. By using the half-life and the initial activity, we can calculate the activity at any given time. In this case, we used the half-life of 1 month and the initial activity of 2 microcurie to find the activity of the sample two months earlier. The activity of the sample decreased by half each month, so after two months, it was reduced to one-fourth of the initial activity. Therefore, the activity of the sample two months earlier was 4 microcurie.