Final answer:
The third layer of the epidermis where the splinter lodged is called the stratum granulosum. This layer is below the stratum corneum and the stratum lucidum, which are the first and second layers, respectively, on the palms of the hands.
Step-by-step explanation:
If a splinter pierces the palm of your hand and lodges in the third layer of the epidermis, it has penetrated into the stratum granulosum. The layers of the epidermis, starting from the outermost to the innermost are: stratum corneum, stratum lucidum (specific to palms and soles), stratum granulosum, stratum spinosum, and stratum basale. In this case, the splinter did not reach the dermis where the blood vessels are, hence there would not be any bleeding. The stratum granulosum layer contains keratinocytes filling with keratin, which is part of the process where these cells start to die, preparing to advance to the next layer. This layer is crucial for providing a waterproof barrier to prevent dehydration of underlying tissues.