**Core Concept**
The question is testing the student's knowledge of the ultraviolet (UV) spectrum, specifically the wavelength of UVB rays. UVB rays are a component of sunlight that play a crucial role in vitamin D synthesis and have been linked to various health effects, including skin cancer.

**Why the Correct Answer is Right**
UVB rays have a wavelength between 290 and 320 nanometers (nm). This range is critical for vitamin D synthesis in the skin, as it is absorbed by 7-dehydrocholesterol, a precursor to vitamin D3. The specific wavelength of UVB rays is essential for initiating the photochemical reaction that leads to vitamin D production.

**Why Each Wrong Option is Incorrect**
**Option A:** 250-280 nm - This range corresponds to UVC rays, which are largely absorbed by the Earth's atmosphere and are not relevant to vitamin D synthesis.
**Option B:** 320-400 nm - This range is characteristic of UVA rays, which are more deeply penetrating and have been linked to skin aging and cancer, but are not primarily responsible for vitamin D synthesis.
**Option C:** 400-450 nm - This range is outside the typical UV spectrum and corresponds to visible light, which is not biologically active in the same way as UVB rays.

**Clinical Pearl / High-Yield Fact**
It's essential to remember that UVB rays are responsible for vitamin D synthesis, and prolonged exposure to UVB radiation can increase the risk of skin cancer and photoaging. Sun protection measures, such as sunscreen and protective clothing, are crucial to prevent these adverse effects.

**Correct Answer:** C. 290-320 nm