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The concept of the particle nature of electromagnetic (EM) radiation is pivotal in understanding the dual traits of light. While we often conceive light as a wave, certain phenomena exhibit its particle characteristics. One seminal example is the photoelectric effect, demonstrating that EM radiation can behave like a stream of particles called photons.

In the photoelectric effect, photons striking a metal surface transfer energy to electrons. If the energy is high enough, it can dislodge the electrons from the surface. Intriguingly, merely increasing the intensity of light does not increase the energy per photon; it just increases the number of photons. The crucial factor is the frequency of the incident light. Below the threshold frequency, regardless of the light's intensity, no electrons are ejected. This crucial observation supports the notion that light, in some scenarios, behaves as having a discrete, particle-like quality.

Quantum theory is a fundamental framework of modern physics that delves into the nature and behavior of matter and energy on the atomic and subatomic levels. It describes an avant-garde picture of reality where quantization, the existence of discrete energy levels, governs the physical properties of particles and fields.

According to quantum theory, light and other forms of EM radiation are quantized into photons. Each photon carries a specific amount of energy that directly correlates with its frequency. This relationship is elegantly encapsulated by the formula \( E = h u \) where \( E \) is the energy of the photon, \( u \) is its frequency, and \( h \) represents Planck's constant. This quantization explains why, in the photoelectric effect, only photons with a frequency above a certain threshold can eject electrons. It is a profound shift from classical physics, which could not adequately explain phenomena at the atomic scale.

Planck's constant, denoted by \( h \), is a crucial element in quantum mechanics, serving as the bridge between the macroscopic and quantum worlds. It signifies the size of the discrete units of energy that can be absorbed or emitted as electromagnetic radiation.

The value of Planck's constant is approximately \(6.62607015 \times 10^{-34}\textrm{Js}\), establishing a small, yet fundamental scale for quantum interactions. Its relevance extends to the calculation of a photon's energy for any given frequency using the equation \( E = h u \) mentioned earlier. Planck's constant is indispensable as it defines the quantum of action or the smallest possible action that can take place in nature. This infinitesimal action underpins the stability of atoms and the emission and absorption of light, influencing every quantum event, including those described by the photoelectric effect.