Question

Why it is impossible to have a perfectly monochromatic source of light

Answer 1

Monochromatic light is a wave with exactly one frequency. If you look for a finite time at a beam of light it can seem as if it has exactly one frequency, however if the light is ever switched off or there was ever a time before it was switched on then this can't be true. A single sine wave goes on oscillating forever and has been oscillating forever.

Heisenberg's uncertainty principle. The wavelength of light is related to it's momentum, and quantum objects (such as light particles) cannot have their momentum defined with infinite precision. That's why a photon cannot have one exact wavelength, instead it has a range of possible values for it's wavelength
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Answer 2

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Suppose that I have a source of monochromatic light of which I can lower that intensity so that it emits one photon, say, per minute. At the other end of the beam I have some kind of photoelectric detector that records the arrival of each photon. It seems like one could construct a detector to record the arrival time of each photon. But the Heisenberg Uncertainty Principle says that because the light is monochromatic (one precise frequency) then we cannot pin down the photons in time. Does that mean that it is impossible to construct a detector to record the “precise” arrival time of monochromatic photons? Ans, yes!!!✌

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