How did the photoelectric effect explain the emergence of quantum theory?

There are several inexpressiveness in classic theory about photoelectric effect such as:
- in classical prediction
electron should absorb energy continually from the electromagnetic waves
and as the light intensity incident on the metal is increased, the electron should be ejected with more linetic energy
-but the experimental results show that:
the maximum kinetic energy is independent of light intensity
and the current goes to zero at the same negative voltage for all intensity curves

-in classical prediction:
for very weak light, a measurable time interval should pass between the instant the light is turned on and the time an electron is ejected from the metal
this time interval as required for the electron to absorb the incident radiation before it acquires enough energy to escape from the metal
-experimental results show that:
electrons are emitted almost instantaneously, even at very low light intensities
and less than 10^-9 sec

-another item is dependence of ejection of electrons on light frequency that in classical prediction, electrons should be ejected at any frequency as long as the light intensity is high enough
but the experimental results show that no electrons are emitted if the incident light falls below some CUTOFF FREQUENCY
no electrons are ejected below the cutoff frequency regardless of intensity
-at last, dependence of photoelectron linetic energy on light frequency that in classical prediction there should be no relationship between the frequency of the light and the electric kinetic energy and the kinetic energy should be related to the intensity of the light
but in fact, the maximum kinetic energy of the photoelectrons increases with increasing light frequency

light waves act like particles,and particles act like waves... it is the energy of the light not the extent of the light..i.e. laser's as per ordinary light.
Matter can go from one spot to another without moving through the intervening space (known as quantum tunneling)