If I purchase a Promethium Mine why can't I take a resource after I have purchased the card, why must I wait a turn. All of the triggering conditions have been met. I should be allowed the one resource once I purchase the card.

This is like you buying a bag of chips and someone telling you that you can't eat them for another hour after you have bought them.

The timing for the reaction ability doesn't allow it.

The text for getting resources off of Promethium Mine is:

" Reaction: After the deploy phase begins, transfer 1[RESOURCE] from this card to your resource pool."

As it says in the RRG (p. 13), "A reaction ability is always used immediately after its triggering condition has occurred and has been resolved. ... Once the opportunity to react to a triggering condition has been passed by both players, further reactions to that specific triggering condition cannot be used."

Since a reaction has to be used immediately after the triggering condition occurs, and both players passing on the opportunity to play reactions to a triggering condition in order to continue game play stops all further reactions to that triggering condition, Promethium Mine can never give you a resource in the same phase in which it is deployed. This is because all players must pass on the opportunity to trigger reactions to the Deploy Phase starting before either of them ever gets a chance to deploy a card in the phase.

In short, you cannot wait to play reactions. You have to use them right away or not at all. It's the reason you cannot deploy Might Wraithknight during the deploy phase and wait until the combat phase to trigger his response.

This is like you buying a bag of chips and someone telling you that you can't eat them for another hour after you have bought them.

Well... trying to trigger Promethium Mine right away is more like expecting the bank to give you your chips when you swing by the ATM on the way to lunch.