We can't work from the serial number alone, as S&W had sever different numbering sequences that were used for different model families.
We can probably answer you question if you give us further details.
Is it a breaktop revolver, or does the cylinder swing out to the side?
What caliber is it?
Are there any patent dates on the top (or side) of the barrel? If so, what is the last one?
How long is the barrel, measuring from the muzzle to the front of the cylinder?
Is there a letter in front of the serial number, possibly separated by several spaces? The letter, if there is one, is part of the serial number.
Pics would help, too, if you could post a couple of snapshots.