Photoelectric emission Law time lag of emission of electrons In Einstein's photoelectric emission Laws it has been described that there is no time lag between the incident light and emission of electrons(as written in my book),however I would like to question that how is it even practically possible because to emit an electron the atoms would  have to absorb the light and it needs  reach it's threshold energy level to emit itself.At first it would vibrate after gaining energy and then it might transfer some energy  to other electrons and all these process have to take at least a few nano seconds so how can this law state that the the electrons are ejected instantly.
Any answers to clear my doubt?
 A: There is no time lag (or very very small indeed). 
What happens is that one photon interacts with one electron. If the energy of the photon is higher than the ionisation energy (the energy required to liberate the electron) the electron is ejected from the material with a kinetic energy equal to the energy of the photon minus the ionisation energy. 
This is a one to one process. You cannot add multiple photons to get enough energy. So it doesn't matter if you just pump more electrons at the material, it still won't photoemit until the energy of the photons are above the ionisation energy of the material. This speaks to the quantum nature of light. Understanding this was what got Einstein his Nobel prize. 
So, now that we know that only one photon will interact with an electron in an photoemission event, (and that the rate at which photons impinge doesn't matter), we can think about the timescale of the interaction. 
It happens so quickly that our electronic clocks simply are incapable of measuring quickly enough. However, EPFL showed that during photoemission, the spin polarization of emitted electrons can be related to the attosecond time delays of photoemission. They did so in a way without the need for any experimental time resolution or measurement — essentially, without the need for a clock. 
To do this, the scientists used a type of photoemission spectroscopy (SARPES) to measure the spin of electrons photo-emitted from a crystal of copper. They determined a delay of one billionth of one billionth of a second in photoemission by measuring the spin of photoemitted electrons without the need of ultrashort laser pulses. This is $1×10^{-18}$ seconds for the event. 
