Alchemists in the middle ages dreamed of converting base metals, such as lead, into precious metals—gold and silver. why could they never succeed? today could we convert lead into gold?

Explanation:

Each element in the periodic table has different but fixed number of the protons in nucleus of it's atom, which is known as the atomic number.

Transmutation of one chemical element into the another involves the changing of the atomic number. Such nuclear reaction requires millions of the times more energy as compared to normal chemical reactions. Thus, the dream of  the alchemist of transmuting the lead into the gold was never achievable chemically .

Conversion of lead to gold in today's world:

This conversion is indeed possible. The requirements are a particle accelerator, tremendous supply of the energy. Nuclear scientists at the Lawrence Berkeley National Laboratory located in California, more than 30 years ago, succeeded in producing very minute amounts of the gold from the bismuth. Bismuth is a metallic element which is adjacent to the lead on periodic table. Same process would work for the lead but isolating gold at end of reaction would prove much more difficult because lead is available in many isotopes. The homogeneous nature of the element means that it is easier to separate the gold from the bismuth as compared to separate the gold from the lead which has four  isotopic identities which all are stable.

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