Faith writes:
I would expect an allele to be the length of the gene. But perhaps I'm wrong about that.
No, you're right about that. Think of a gene as one slot on a chromosome. Each chromosome has slots for lots of genes. Each gene has a number of alleles that can be plugged into its slot. There is no requirement that all alleles of a gene be the same length in terms of nucleotides, but it would probably be generally correct to say that most alleles of the same gene are approximately the same length.
Each allele of a gene consists of a sequence of nucleotides. A point mutation is when a copying error causes one of the nucleotides to be incorrect. It would be like changing one letter of the word COW to get SOW. Continuing the analogy, whereas before the mutation the allele performed the action "MILK THE COW", after the mutation it performs the action "MILK THE SOW".
So the question is, are you looking for an explanation of how a point mutation (single nucleotide substitution) is actually the same thing as a new allele? If so, then I think I just provided one.
--Percy