The amendment that is involved in this scenario is the 4th Amendment.  However, none of Mrs. Jones’s rights have been violated.

The 4th Amendment protects us against unreasonable searches and seizures.  It says that the police must, in general, have a warrant to search a person, that person’s possessions, or their home.  They must also have a warrant (in general) to seize the person or the person’s property.  This amendment could conceivably prevent the police from seizing the bomb and arresting Mrs. Jones.

However, the police have done nothing wrong in this instance.  Mrs. Jones consented to allow the police into her house.  The police did not search the house.  Instead, while legally in the house, they saw the bomb in plain sight.  Your scenario states that the police officer saw the bomb while he or she was simply sitting in the living room.  This means that the officer was not actively searching.  Officers may seize evidence if a crime so long as it is in plain sight in a place where the police have a legal right to be.  Since they have been allowed into the house by Mrs. Jones, and since they have not conducted any search of the house, none of Mrs. Jones’s rights have been violated.