NASA`s Deep Impact space mission was employed to take detailed pictures of the comet nucleus named Tempel 1. The correct answer is Option 4.

Deep Impact was a NASA mission launched in January 2005 with the primary objective of studying the interior of a comet. Its target comet was Tempel 1, a short-period comet that orbits the Sun approximately every 5.5 years.

The mission involved a specialized spacecraft that was designed to release a projectile, called an "impactor," onto the surface of the comet. The impactor was meant to create a controlled collision with the comet`s nucleus, generating a crater and ejecting material from beneath the surface. This would allow scientists to study the composition and structure of the comet.

On July 4, 2005, the impactor was successfully released, and it collided with Tempel 1, creating a bright flash and a visible impact plume. The event was observed by the Deep Impact spacecraft itself, which captured detailed pictures and spectra of the impact and its aftermath. These observations provided valuable insights into the comet`s composition, revealing information about its surface and subsurface layers.

The data collected during the Deep Impact mission significantly contributed to our understanding of comets and their role in the formation of the solar system. The images and measurements obtained from Tempel 1 provided scientists with important data about the comet`s structure, surface features, and composition, including the presence of water ice and various organic compounds. This knowledge helps scientists piece together the puzzle of how comets form and evolve.

It`s worth noting that Halley`s Comet (Option 1), Hale-Bopp (Option 2), and Hyakutake (Option 3) are all famous comets that have been observed and studied by various missions and telescopes, but they were not the specific targets of NASA`s Deep Impact mission.