How much an 1898 Queen Elizabeth front eagle at the back silver coin 1 dollar?

Please check your coin.

Queen Elizabeth II was not born until 1926 and did not become queen until 1953.

What you probably have is an AMERICAN $1 piece called a Morgan dollar in honor of its designer. The woman on the front is a representation of Miss Liberty. There's more information at the question "What is the value of an 1899 US silver dollar?".