Which scale allows the performer to play all the white keys from F to F?

The correct scale that allows the performer to play all the white keys from F to F is the Lydian Mode. The Lydian Mode is based on the fourth degree of the major scale and is characterized by its raised fourth note. In the case of starting on F, the notes would be F, G, A, B, C, D, E, and again F, which are all the white keys on the piano.

This mode provides a distinct sound compared to other modes, as the raised fourth creates a unique and bright quality that differentiates it from the Ionian (Major) scale. The Ionian Mode, while also played on the white keys from C to C, does not start on F, and thus does not fit the criteria of the question. Similarly, the Mixolydian and Phrygian modes would utilize different note sequences, leading to different keys and tonalities that do not correspond to the F to F range strictly on white keys. Therefore, the Lydian Mode is the correct choice.