Final answer:
After meiosis I, each nucleus in an organism with a chromosome number of 2n=12 will have 6 chromosomes. The organism can produce 64 unique gametes based on independent assortment alone.
Step-by-step explanation:
During meiosis in an organism with a chromosome number 2n=12, each nucleus will have 6 chromosomes after meiosis I. This is because meiosis I separates homologous chromosomes into two daughter cells, reducing the diploid number (2n) by half to the haploid number (n).
Based on independent assortment alone, the number of unique gametes that can be produced is calculated with the formula 2^n where n is the number of homologous chromosome pairs. Thus, for an organism with a set of 6 chromosomes (n=6), there would be 2^6 or 64 unique gametes possible from independent assortment, not taking into account the additional variation introduced by crossing over.