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Question

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Long ago people tried to change inexpensive metals, such as lead, into gold. What fundamental principle of matter did these people fail to understand?

Answer 1

to change lead into gold, or any element into another element, you have to change the number of protons in the atom's nucleus.

The nucleus of an atom is held together by the Strong Nuclear Force. This is the fundamental principle not understood by historical alchemists.

As far as I know the the Strong Nuclear Force is only broken by naturally occuring nuclear decay and highly energetic reactions such as Nuclear Fission and Fusion

Answer 2

That's the point, alchemists had no fundamental principles of matter. Unlike later scientists, alchemists never had the inclination to separate the physical aspects of their craft from the metaphysical interpretations. They never understood the actual atomic structure of the elements or could even concieve of the actual nuclear manipulation required to turn an atom of lead into an atom of gold.

The best known goals of the alchemists were the transmutation of common metals into gold or silver (less well known is plant alchemy, or "spagyrics"), and the creation of a "panacea," a remedy that supposedly would cure all diseases and prolong life indefinitely. European alchemists invested much effort on the search for the "philosopher's stone", a legendary substance that was believed to be an essential ingredient for either or both of those goals. The philosopher's stone was believed to mystically amplify the user's knowledge of alchemy so much that anything was attainable. They came to view these metaphysical aspects as the true foundation of alchemy; and chemical substances, physical states, and material processes as mere metaphors for spiritual entities, states and transformations. Thus, both the transmutation of common metals into gold and the universal panacea symbolized evolution from an imperfect, diseased, corruptible and ephemeral state towards a perfect, healthy, incorruptible and everlasting state; and the philosopher's stone then represented some mystic key that would make this evolution possible. Applied to the alchemist himself, the twin goal symbolized his evolution from ignorance to enlightenment, and the stone represented some hidden spiritual truth or power that would lead to that goal.

Alchemists enjoyed prestige and support through the centuries, though not for their pursuit of those goals, nor the mystic and philosophical speculation that dominates their literature. Rather it was for their mundane contributions to the "chemical" industries of the day—the invention of gunpowder, ore testing and refining, metalworking, production of ink, dyes, paints, and cosmetics, leather tanning, ceramics and glass manufacture, preparation of extracts and liquors. Modern chemistry in the 18th and 19th centuries, based on revolutionary discoveries of Lavoisier and John Dalton — finally provided a logical, quantitative and reliable framework for understanding matter transmutations, and revealed the futility of longstanding alchemical goals such as the philosopher's stone.

Matter transmutation, the old goal of alchemy, enjoyed a moment in the sun in the 20th century when physicists were able to convert lead atoms into gold atoms via a nuclear reaction. However, the new gold atoms, being unstable isotopes, lasted for under five seconds before they broke apart.

Answer 3

They were trying to make atomic changes by manipulating molecules.

Answer 4

they failed to understand elements. The fact that you cannot break down certain items (other then sub-atomic particles).