True, but 4-6 feet from a 400 watt MH will very likely be far less than 20k lumens.
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My 600 watt hps can sit at 18-24 inches from (mature plants, not seedlings) plant tops and I get anywhere from 30k-50k lumens. My target for mature plants is around 40k. - personal preference I guess. I like my seedlings to be around 20k lumens until they get about 4-8 inches tall, then I like to increase. (I do this under 2x 4' T5 bulbs that are about 9 inches from brand new seedling tops - plants that just broke ground)
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4-6' is definitely safe for seedlings, maybe even overly safe. I think you would be perfectly fine being closer to 2-3 feet, but that is as long as you don't over heat the plants and the plants can handle the intensity. Your plants look to be right at the cusp of being able to take on real lighting (well most of them). If you just put them under a 400 watt mh after being under a fluoro their whole life, they may not like the drastic change, but if you acclimate them (lower the MH light slowly) you could in theory almost touch the plant tops as long as it doesn't get too hot (which it would be super hot, thus people never get that close).
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And juanitos is correct, they don't
need to be that close, but they
can be that close and the chances of hurting your plants at 2-3 feet are slim, as long as 1) it's not a drastic change and 2) the temps stay regulated.
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You will get more out of your plant with higher lumens, but I'm used to pushing canna plants to get the most out of them. People don't usually need to push pepper plants too hard though.
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edit: I'd suggest to put the biggest plants in the center, that is where you get the most lumens (the bigger ones can handle more), that way the ones that can utilize the light the best get the most and the smaller ones that may not like that much light can be at ease. Put the smaller seedlings on the outside until they get a little bigger. Once they're all bigger, I would move the bigger ones to the outside and the smaller ones in the center to get a nice bowl-shaped canopy to even out the amount of lumens they all get.
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Read the plants - if they start to wilt at any point under the new light, they may be too close (or, too hot).