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There is nothing dangerous or destructive happening when your copper pipes turn Green / Blue neither are they deteriorating.
Nignthoujam Sandhyarani ties it up very nicely as follows:
Copper oxidizes whereby it turns Blue / Green. Oxidation is a phenomenon whereby an element loses electrons (and/or hydrogen) on interacting with another element. There are many examples of oxidation, which we observe in our day-to-day life. To mention a few; there is oxidation of iron, aluminum and even, a freshly cut apple.
Oxidation of iron, referred to as 'rust', leads to corrosion and/or formation of a flaky, reddish outer layer. Another example is the oxidation of aluminum, leading to formation of white, flaky layer. This is usually seen in aluminum doors and windows after a heavy rainfall. When an apple is cut and the cut surface is exposed to air, it turns brown. This is nothing but oxidation.
Similar to iron and aluminum, the element copper undergoes the process of oxidation, if it is exposed to air. Copper metal reacts with oxygen, resulting in the formation of copper oxide, which appears green in color. It is to be noted that copper does not react with water. The outer green layer, formed after the oxidation of copper, is known as patina.
Unlike other destructive oxidation, patina acts as a protective layer. This is the reason as to why, copper is considered as an important metal, resistant to corrosion. The patina prevents further corrosion of copper beneath the oxidized layer. Very often, patina is seen on the roofs of old buildings, which acts as a waterproofing layer.
The function of patina as a protective layer can also be seen in the Statue of Liberty. According to the Copper Development Association, the oxidation of the statue's copper skin is only about 0.005 inch till now. For preventing oxidation, the best way is to protect the surfaces, that are likely to be exposed to air and water, with the help of a protective coat. This way, the surface of the metal is prevented from reacting with oxygen and/or water.