Animated Solution for Physics - Dual Nature of Matter and Radiation: The time taken by a photoelectron to come out after the photon strikes is approximately

This question might seem like a simple memory-based fact, but it actually holds the key to one of the greatest revolutions in modern physics. Let's dive into the story behind this incredibly tiny number.

Before Einstein stepped in, physicists believed light was purely a wave. Imagine a wave of water hitting a beach. The energy of the wave is spread out over its entire wavefront. If light were a wave, its energy would be continuously distributed over the area it illuminates.

Now, imagine a single electron sitting on the surface of a metal, waiting to absorb enough energy to break free (its work function). If the incident light is very dim, the wave theory predicts that the electron would have to wait, soaking up energy like a sponge, until it finally has enough to pop out. Calculations showed that for very faint light, this process could take minutes or even hours!

However, experiments showed something completely different. No matter how dim the light was, as long as its frequency was above the threshold, electrons were ejected instantly. There was absolutely no measurable time delay. This was a massive contradiction that classical physics simply could not explain.

Einstein solved this by proposing the particle nature of light. He suggested that light travels in discrete packets of energy called photons. When a photon hits the metal, it doesn't spread its energy around. It collides with a single electron in a one-to-one interaction. The electron absorbs the entire photon's energy in a single, instantaneous gulp.

Because it's a direct particle-to-particle collision, the emission happens immediately. But in physics, 'instantaneous' still takes some time, dictated by the scale of atomic interactions.

Experimentally, the time delay between a photon striking the surface and the photoelectron being ejected has been measured to be on the order of $10^{-10}$ seconds (or $0.1$ nanoseconds). To put that in perspective, $10^{-10}$ seconds is to one second what one second is to over $300$ years!

So, while it's not mathematically zero, for all practical macroscopic purposes, the photoelectric effect is an instantaneous phenomenon, beautifully proving the quantum nature of our universe.