The short answer is "1921", but within that year the prize for the most valuable circulated half depends on its condition and mint mark.
In lower grades the 1921-D half is most valuable, with retail prices as of 05/2011 in the range $270 for a very worn coin. At the opposite end, retail prices are about $3200 or more for one that shows only traces of circulation wear.
1921-S halves are more common in lower grades and scarcer in higher ones, with very worn ones selling for an accessible $50 while a barely-worn one will bring $8000 to $13,000.
Average circulated Walking Liberty half dollars from 1940 to 1947 regardless of Mintmarks are valued at $14.00.
1939 is a common date for Walking Liberty halves. Most circulated coins are valued for the silver, about $12.00.
There is no such coin, but a WALKING LIBERTY half dollar dated 1941 with no mintmark in circulated condition runs from $8.00-$30.00.
Assuming it's circulated and has no mintmark. Values for average circulated Walking Liberty coins are $16.00-$75.00.
If you look on the back of the coin it will say 50 cents not a dollar. The coin is a Walking Liberty Half Dollar, most circulated examples are valued for the silver content only at about $5.00 Uncirculated coins can be $25.00 or more.
Average circulated Walking Liberty half dollars from 1940 to 1947 regardless of Mintmarks are valued at $14.00.
1939 is a common date for Walking Liberty halves. Most circulated coins are valued for the silver, about $12.00.
Assuming it's circulated and has no mintmark. Values for average circulated Walking Liberty coins are $16.00-$75.00.
There is no such coin, but a WALKING LIBERTY half dollar dated 1941 with no mintmark in circulated condition runs from $8.00-$30.00.
If you look on the back of the coin it will say 50 cents not a dollar. The coin is a Walking Liberty Half Dollar, most circulated examples are valued for the silver content only at about $5.00 Uncirculated coins can be $25.00 or more.
The 1946 walking liberty half is a common date, but because it is 90% silver, it is worth around $10.50 in common circulated condition.
All Walking Liberty Half dollars from 1940 to 1945 regardless of any mintmark have the same value of $12.00 in average circulated condition.
Look at the coin again, it's a Walking Liberty half dollar not a dollar and is a very common date with low retail values of $15.00-$16.00 for most circulated coins. No US dollar coins exist dated 1942.
$7.50 in bad circulated condition, $8.50 in average circulated condition, $15 in good circulated condition, and $49 in uncirculated condition.
Please look at the coin again it's not a dollar it's a half dollar with retail values of $7.00-$9.00 in average circulated condition.
8-10-11>>> Assuming the coin is circulated and has no mintmark, the 1935 Walking Liberty half dollar is a common coin with a retail value of $18.00 for average circulated coins.
The 1943 Walking Liberty half dollar is the high mintage of the series with an average value of $5.00 to $8.00 in circulated condition.