A substance has a half of 3mins. after 6mins. the count rate was observed to be 400. What was its count rate at zero time?

The count rate of a substance is directly proportional to the amount of the substance present. The half-life of a substance is the time it takes for half of the substance to decay. In this problem, we know that the half-life of the substance is 3 minutes. This means that after 3 minutes, half of the substance would have decayed, and after another 3 minutes (total of 6 minutes), another half of the remaining substance would have decayed, leaving only a quarter of the original substance. We also know that at 6 minutes, the count rate was observed to be 400. This count rate corresponds to a quarter of the original substance because half of the substance decayed in the first 3 minutes and another half decayed in the next 3 minutes. Therefore, the count rate at zero time (when all of the substance was present) would have been four times the count rate observed at 6 minutes, which is 4 times 400 = 1600. Therefore, the correct answer is 1600.