 PPM is a term used in chemistry to denote a very, very low concentration of a solution. One gram in 1000 ml is 1000 ppm and one thousandth of a gram (0.001g) in 1000 ml is one ppm.
One thousanth of a gram is one milligram and 1000 ml is one liter, so that 1 ppm = 1 mg per liter = mg/Liter.
PPM is derived from the fact that the density of water is taken as 1kg/L = 1,000,000 mg/L, and 1mg/L is 1mg/1,000,000mg or one part in one million. (In case of solutions)
Similarly, in case of solids 1 ppm = 1 mg/Kg of that solid.
Therefore, in case of Lead nitrate, 1 ppm solution (I think this should be 1 ppm of Lead-Pb and not Lead mitrate), please consider folllowing calculations,
Lead nitrate Pb(NO3)2 - Molecular weight = 331.2, Atomic weight of Lead (Pb) = 207.2
Hence, 207.2 mg is equivalent to 331.2 mg Lead nitrate
and therefore, 331.2/207.2 = 1.598 = 1.60 mg of Lead nitrate in 1000 mL is 1 ppm lead solution (And NOT Lead nitrate solution. (You can do serial dilutions of stock solutions of Lead nitrate of 160 mg in 100 mL. Dilute this 10 mL to 100 mL, further dilute this 10 mL solution to 1000 mL to get 1.60 mL in 1000 mL. This is 1 ppm Pb Lead solution.
Similarly, 3.312 mg of Lead nitrate dissolved in 1000 mL is 1 ppm Lead nitrate solution. This can be prepared by serial dilutions as above to get 1 ppm Lead nitrate Pb(NO3)2 solution.
Hope I have explanied you to understand the concept of ppm solutions and its calculations.

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Thank you so much sir

You are welcome.