7th week in 1984. Depending on how the other chips average out, you're looking at a machine that is made somewhere between Feb. and March of 1984.
Which Apple IIe is this since I notice you posted a couple of them up.
EDIT:
Not all Apples have this but above the power jack/port of the motherboard, along the edge, there is a white square with rounded corners (see the pic I posted above). Sometimes They stamp a date code on it, in the case of this pic above it is 4383 or the 43rd week of 1983, which would make it October of 1983.
Thing is this - a lot of times the date codes on the chips may not match the date code on the mother board. This is because Apple bought the chips in bulk and the boards were not prepared at the time, so the chips can be older than the board itself. Most of the time they average out to the same time area, but the board posted in the pic has older chips (early 1983) compared to the board (later 1983).
And Apple did not post a date on all their board. I'm thinking that this might be a diagnostic test date - an Apple pulled out of assembly line and then tested before being put back on the pile to sell. This would make more sense as it explains why not every board is dated and this one was dated.
But why such a huge gap in the dates? One of the tests I remember was the 1000 hour burn test. 1000 hours is about a month and a 1/2. And other tests (like the slot/disk drives) are 100 hour tests, which is about 4 days. But again, this would explain why there is a huge gap between the dates on the chips and the board.