Final answer:
The effector molecule for the Trp repressor of the trp operon is tryptophan. It binds to the Trp repressor, changing its shape and allowing it to bind to the operator, thus preventing transcription of the downstream genes.
Step-by-step explanation:
The effector molecule for the Trp repressor of the trp operon is tryptophan. In prokaryotic cells, the trp operon is a repressible operon, meaning that it is normally switched on and actively transcribing genes unless tryptophan is present. When tryptophan binds to the Trp repressor, it changes its shape, enabling it to bind to the operator, which prevents RNA polymerase from transcribing the downstream genes.