There are chemical tests for silver and gold purity, but they can damage the items you are testing.  Here are some "non-destructive" tests:

You will need a very accurate scale to get the weight of the coin. 1/100 of gram would be good, 1/1000 of a gram is better.  Obtain an accurate weight of the coin.  You can then see if it matches charts in reference books or even other coins that you have.

You will also need an accurate way of measuring water volume.  You may use a glass beaker or graduated cylinder ( like those used in a lab ). You can measure exact volumes in milliliters (cc).  With a beaker, fill it with water to a certain level exactly (example 100.00 milliliters).  Drop  in the coin and measure the level of the beaker (example 100.25 ml).   Volume  of coin is (measurement minus starting volume is coin volume:  100.25-100.00=0.25 ml).  This is where you may want to use a syringe instead, to draw off the water and bring the level in the beaker down to 100.00 ml.  Read how much water is in the syringe (example: 0.25 ml).

Take the weight in grams and divide by volume in ml and this give you how much the object weighs per ml.  This can give you the density (g/cc).  Silver is much more dense than copper.  If you take a coin that you know is 0,750 silver, you can perform this test and know how much this alloy weighs per ml.  Do this for 0,500  0,600  0,800 0,900 0,950 and 0,975 coins that you know are real.  You can make a chart of the results.  Then when you test a coin you can compare to the chart to see how much silver is in it.  You can do the same for gold, which is even more dense than silver.

You can get a black light (ultra violet) from a stamp dealer (around $20, do not use the cheap light bulbs for $4, they are not the same).  They use it to see "tagged" stamps.  Tagging is used by automatic machine to process mail.  Many Canadian stamps glow under a black light.  Many other things show up as well under a black light:
Enamel repairs, stains on stamps and paper money, differences in ribbons, certain types of glue, certain types of paper will appear to change colour and more.  Go to a dark place and look at these things under the black light,  Some thing will appear dark and other things will glow bright shades of yellow, green, orange and other colours.  This is where you can put an original item beside a possible fake and examine for differences.

Don't over do it. UV light is the part of sunlight that fades things.  Test items only a few times to avoid damage, not really to the item, but mainly your eyes.  Do not do this for more than a few minutes at a time.  Do not look directly at the bulb.

Use also a vernier caliper for measuring dimensions.  Another tip is to place two items (original and the one you are testing) side by side or back to back and compare.

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