Spectrum of LEDs

You will be getting a narrow band, many LEDs have width of about 20 nm at 50% down from the peak; other LEDs have quite a wide band. The datasheets for LEDs will give you a curve for those specific to a particular LED.

Here are the graphs of LEDs I chose for a scientific imaging project based on how narrow their bands were without resorting to exotic components. I wanted a selection of colours as narrow as possible (but cheap), and bought well-known manufacturers' parts with datasheets, which I summarised as follows:

(The 400 nm line is dotted because it was an estimate. The others were traced from datasheets and normalised to give same height.)

If you need narrower:

• a laser will be better than 1 nm, and can be much much better. (Given as 0.85 in datasheet of cheapest laser at a distributor). Some "broadband" lasers have a linewidth of a few to about 10 nm (Wikipedia)
• some extrenely narrow bandpass filters are available, such as astronomical sodium filter, which can have a typical bandpass of 0.05 nm. Be warned they can be extremely expensive.