Photoelectric effect and Plank's theory

The photoelectric effect is the emission of electrons (called "photoelectrons") from a surface when light is shined on it. It was first observed by Alexandre Edmond Becquerel in 1839, although credit is usually reserved for Heinrich Hertz, who published the first thorough investigation in 1887. Another, particularly thorough investigation was published by Philipp Lenard in 1902.Einstein's 1905 paper discussing the effect in terms of light quanta would earn him the Nobel Prize in 1921, when his predictions had been confirmed by the experimental work of Robert Andrews Millikan. To put it another way, in 1921 at least, Einstein's theories on the photoelectric effect were considered more important than his theory of relativity (a name coined, as it happens, by Max Planck).
Prior to Einstein's paper, electromagnetic radiation such as visible light was considered to behave as a wave: hence the use of the terms "frequency" and "wavelength" to characterise different types of radiation. The energy transferred by a wave in a given time is called its intensity. The light from a theatre spotlight is more intense than the light from a domestic lightbulb; that is to say that the spotlight gives out more energy per unit time (and hence consumes more electricity) than the ordinary bulb, even though the colour of the light might be very similar. Other waves, such as sound or the waves crashing against a seafront, also have their own intensity. However the energy account of the photoelectric effect didn't seem to agree with the wave description of light.
The "photoelectrons" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured. This kinetic energy (for each photoelectron) is independent of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a kinetic energy for the photoelectrons of zero or less), no photoelectrons are emitted at all, however intense the light source. Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy, rather than the same number of photoelectrons to be emitted with higher kinetic energy.
Einstein's explanation for these observations was that light itself is quantized; that the energy of light is not transferred continuously as in a classical wave, but only in small "packets" or quanta. The size of these "packets" of energy, which would later be named photons, was to be the same as Planck's "energy element", giving the modern version of Planck's relation: E=hv

Uncertainty principle
The Planck constant also occurs in statements of Werner Heisenberg's uncertainty principle. Given a large number of particles prepared in the same state, the uncertainty in their position, Δx, and the uncertainty in their momentum (in the same direction), Δp, obey

where the uncertainty is given as the standard deviation of the measured value from its expected value. There are a number of other such pairs of physically measurable values which obey a similar rule. One example is time vs. frequency. The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in Fourier analysis), rather than the compromises and grey areas of time series analysis. A practical example is computational neurology trying to both measure the time effect and frequency of a neuron burst. fMRI (functional MRI), whose signal processing is based on Fourier transforms, can resolve frequency, but not time (a limit of Fourier analysis due to uncertainty). An EEG (a time series analysis measurement tool) can resolve time, but not frequency. Due to uncertainty, these are not problems with the design of the measuring instruments, but problems with the nature of quantum measurement and particle realities themselves.
In addition to some assumptions underlying the interpretation of certain values in the quantum mechanical formulation, one of the fundamental corner-stones to the entire theory lies in the commutator relationship between the position operator \hat{x} and the momentum operator \hat{p}