Final answer:
The sun always illuminates half of the moon, as it is a sphere with one side facing the light and the other side in shadow.
The moon phases we see from Earth are due to the viewing angle and not the amount of illumination the moon receives.
Therefore, the correct answer is: option d). one-half
Step-by-step explanation:
The sun illuminates half of the moon at all times, regardless of the moon's phase from our perspective on Earth.
This is because the moon is a spherical body and, just like any sphere in space, it has one side that faces the sun and receives light, while the other side is in shadow.
What changes during the lunar cycle is our view of the moon's illuminated and dark portions from Earth, not the actual amount of illumination the moon receives.
During its orbit around Earth, we observe phases of the moon, which include new, first quarter, full, and third quarter phases.
Each of these is a result of the changing angle between Earth, moon, and sun. Even when we observe a new moon phase and the side of the moon facing Earth is in darkness, the other half of the moon is still fully illuminated by the sun.
Conversely, during the full moon phase, the side of the moon facing us is entirely lit up, yet still, only half of the moon's total surface is illuminated.