Several varieties of Liberty Seated quarters were minted in 1873. You'll need to check whether there's a small mint mark letter on the back, whether there are arrows on either side of the date, and if it does not have arrows, whether the "3" in the date is nearly closed so it almost looks like an 8 or if the points of the 3 are more open.
Numismedia lists the following approximate retail values as of 02/2010:
No mint mark (Philadelphia), no arrows, closed 3:
Very worn condition - $300
Moderately worn - $570
Slightly worn - $780
Almost no wear - $4,458
Uncirculated - $13,440 to $51,350 depending on quality
No mint mark, no arrows, open 3:
Very worn condition - $1,873
Moderately worn - $43
Slightly worn - $59
Almost no wear - $256
Uncirculated - $360 to $8,560
No mint mark, arrows
Very worn condition - $22
Moderately worn - $32
Slightly worn - $68
Almost no wear - $434
Uncirculated - $870 to $7,610 depending on quality
"CC" mint mark (Carson City), arrows:
Very worn condition - $2,700
Moderately worn - $12,300
Slightly worn - $17,700
Almost no wear - $48,004
Uncirculated - $87,500 to $156,250
"S" mint mark (San Francisco), arrows:
Very worn condition - $32
Moderately worn - $90
Slightly worn - $210
Almost no wear - $736
Uncirculated - $1,650 to $26,880
A 1765 US quarter does not exist.
The first US quarter was struck in 1796.
No US quarters were struck in 1922. The US did not make ANY quarters dated 1922.
Certainly the single rarest US quarter is an 1866 proof version - only one of these was struck, and it's impossible to put a value on it. The quarter with the highest market value is a 1795 Draped Bust variety with a small eagle on the back. As of 02/2011 a top-quality one is priced around $450,000. Several other quarters fall in the $250,000-$550,000 range, including 1805 and 1873-CC.
The coin is a 2001 Vermont State Quarter, it's 25 cents.
A US quarter has a face value of 25 cents.
A 1765 US quarter does not exist.
The 1873-CC U.S. quarter dollar has a mintage of 4000 of which only 4 are known to still exist.
From 1873 to 1964. U.S. quarters have the same weight of 6.25 grams.
made 1888
The first US quarter was struck in 1796.
No US quarters were struck in 1922. The US did not make ANY quarters dated 1922.
I assume you want to know what the rarest quarter is, either in terms of mintage or value. By mintage, it's a tie for the 1873-CC and 1827 issues with only 4,000 of each struck. For value, it would almost certainly be a quarter dated 1804 (not to be confused with the legendary 1804 $1 coin) that sells for nearly a half-million in top condition.
Certainly the single rarest US quarter is an 1866 proof version - only one of these was struck, and it's impossible to put a value on it. The quarter with the highest market value is a 1795 Draped Bust variety with a small eagle on the back. As of 02/2011 a top-quality one is priced around $450,000. Several other quarters fall in the $250,000-$550,000 range, including 1805 and 1873-CC.
The coin is a 2001 Vermont State Quarter, it's 25 cents.
Retail value runs $180.00-$400.00 for circulated coins
No US quarters were made in 1810.