Why don't phosphorescent molecules just immediately re-emit the original UV photon? The energized electron of a phosphorescent molecule is said to be 'trapped' in its excited state, because it has to undergo one (or more?) 'forbidden' transitions to get back down to it's original ground state.
But why was it so easy to put it into the excited state in the first place?
Why isn't the initial excitation of the outer electron 'forbidden'?
How can large numbers of  phosphorescent molecules be excited in a split second or so?  Why don't they need time to be excited, just like they need time to be 'de-excited'?
Do some phosphorescent (and fluorescent) molecules immediately re-emit the original UV phtons?
 A: You use the phrase phosphorescent molecule but phosphorescence is normally seen in solids where there are many interacting molecules. When you excite electrons in a solid they will generally decay in a radiationless manner, usually by transferring their energy to vibrations of the lattice (i.e. heat). It is unusual for excited states in solids to decay by emission of a photon.
In phosphorescence the initial excited state decays by transferring energy to the lattice, but in a small fraction of the decays only some of the excitation energy is lost and the electron gets trapped in a long lived lower energy state that:
a) does not easily transfer energy to the lattice
b) has a forbidden transition to the ground state
It is the slow decay of the electrons in these states that produces the light associated with phosphorescence.
So the initial state produced when light is absorbed is not the same as the phosphorescent state. That's why the initial excitation can be fast and efficient while the decay of the phosphorescent state is slow and forbidden. A consequence of this is that the emitted light has a longer wavelength than the absorbed light.
A: Molecule when excited via photon, there is abrupt change in dipole moment ( photon has electric and magnetic part that changes the dipole of the molecule) and absorption of photon is very fast along with change in spin in phosphorescent molecules. When molecule is in excited state ( typically triplet in phosphorescent molecules), it undergoes internal conversion and de-excites to lowest vibrational state of a particular excited electronic state and now it is trapped there. It needs to relax to ground state but the transition is forbidden ( during absorption, scenario was different and molecule had to excite quickly, u can check the time period for different processes) . Trapped molecule will de-excite slowly to ground state through a number of process. Radiative decay will release a photon whole non radiative decays typically releases a phonon.
In conclusion, two process are different with one has to occur very fast while the de-excitation takes time as no abrupt change is occuring in the molecule.
