What is the thickness of a dime?
The actual thickness of a dime is between 1.35 and 1.40 mm.
Atoms vary in size, so let's go with carbon, which is a very common element. A carbon atom is 340 picometers across, or 340 billionths of a millimeter. By comparison a dime is about 18 millimeters across and 1.35 millimeters thick. This means that, by diameter, a dime is about 53 million times larger than a carbon atom. Even the thickness of a dime is about 4 million times the diameter of a carbon atom.
If the coin is the same thickness as a normal dime, it's not copper. It's been plated or exposed to heat/chemicals that changed its color. In this case it's just a damaged dime. However, if the coin is thinner than a normal dime, it could be a lamination error. That happens when the outer cupronickel layer comes "unstuck", like taking the cookie part off an Oreo. The copper core then becomes visible. In this case…
If the coin is the same thickness as a regular dime it's been plated and is only worth face value. If it's thinner than a regular dime and is copper on one side only, the cupronickel cladding un-bonded from the core. This is called a lamination error and is worth around $5 or $6 Note there's no such thing as a 1967-P dime because US coins dated 1965, 1966, and 1967 don't carry mint marks.
Assuming it's the same thickness as a normal dime, you have what's called a "flan". This error occurs when a coin blank accidentally slips into the bin with coins that have already been struck. If your flan has a smooth edge, it's worth about $1. If it has upturned edges like a regular coin but no design, it's worth about $2.