if i adopted a child and then after seven years the mother wants to visit him does she have any rights to do so?

Typically not. Once a parent's parental rights are terminated to make the child legally free for adoption, then that's the end of all parental rights. So technically she has no rights. Any contact with the child would be entirely at your discretion.

The only exception would be if there was some provision in the adoption decree requiring on-going visits. Even so, that she has failed to exercise visits for 7 years should negate any ability to demand future visits.

Legally, you are the child's parent. If you do not believe that it is in your child's best interests to have contact with the birth parent, then just say so.