There is a widespread belief that there is an optimal K value for photosynthesis, and it is 6500.
The K rating of lights does not tell the spectrum of the light per se, but rather just indicates the general colour hue of the light. It has some use for indicating for white lights; whether the light's colour hue is warmer (lower K numbers) or cooler (bluish - higher K numbers). It does not indicate whether the light is suitable for plant growth or not. You will need to look at the PAR values and spectrum curves to determine if the light is good for growing plants.
6500k does not tell us the strength of the light or what the exact spectrum distribution is. It most certainly does not indicate that the light has a similar spectrum to sunlight. This is the reason why indoor lighting is so different from sunlight - something every photographer knows and needs to compensate for.
Below, you can see the various tanks we have grown with lights of various K rating. In fact, the best custom light we have used is 3600k. Above, the hardscape diorama used 4200K rated lighting.
Websites and commercial lighting still like to use K rating as a marketing sales pitch - but it's marketing speak and nothing more.
It is also important to note that the K rating that the scientific community use to determine colour temperature for black body radiators is different from the K rating that the light industry uses (CCT/colour correlated temperature).
Read more here on exactly on how K rating is derived.
Grown with 3600K rated lighting:
Grown with 4200K Lighting:
Grown with 12000K lighting:
Grown with 12000K Lighting:
What determines a good light is its PAR value at a given depth, which gives an estimation of the strength of the light with regards to photosynthesis. Additionally, having a light with favourable spectrum gives better visual color rendering as well as better pigmentation and growth forms. Neither of these can be derived from the K rating value alone. To understand these 2 values, you need to read the PAR charts and spectrum charts associated with the light in question.
Head here to learn more about aquarium lighting for planted tanks
Head here to learn more about PAR values.
Head here to learn more about spectrum curves.