Please read both of these articles regarding electrochemical reduction and toothpaste:
© Electrochemical (Galvanic) Reduction
This process uses an aluminum or aluminum alloy plate and a warm solution of sodium carbonate (washing soda). When the object comes into contact with the plate in the solution, it removes only light tarnish, not the thick, black tarnish produced by years of neglect. Pitting of the object can occur if the aluminum plate is not periodically cleaned. Another not-so-obvious problem is scratching of the object when in contact with the plate.
Objects cleaned by this method may tarnish more quickly than silver that has been polished, for the object’s surface will act like a sponge and more readily absorb tarnish-producing gases and moisture. The solution can also seep into hollow areas such as coffeepot handles, unsoldered spun beads around the tops of lightweight holloware, weighted pieces with minute holes, and any porous attachments. For these reasons, this cleaning technique is not recommended.
© Never Use Toothpaste as a Silver Polish
Toothpaste should NEVER be used as a silver polish. Some toothpastes contain baking soda or other ingredients which are much too abrasive; even trace amounts can cause serious damage. Use polishes that are specifically formulated to remove tarnish from silver.