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Quantum mechanics is a fundamental theory in physics that provides the underlying framework to understand the properties and behavior of matter and energy on the atomic and subatomic level. Unlike classical mechanics, which deals with the macroscopic world's predictable and determinable nature, quantum mechanics embraces the probability of events and the inherent uncertainties of the microscopic world.

At the heart of quantum mechanics is the notion that energy is not continuous, but rather comes in discrete units or 'quanta'. This was a radical departure from the continuous, wave-like behavior of energy that had been originally postulated. Experiments like the photoelectric effect provided concrete evidence that supported the quantum theory, showing that light could behave as both a wave and as a collection of particles known as photons.

The understanding of quantum mechanics is crucial for explaining phenomena that cannot be accounted for by classical physics, such as the stability of atoms, the behavior of semiconductors, and the properties of lasers. Its principles are also key to modern technologies like transistors and microchips, which are essential components of electronic devices.

Wave-particle duality is one of the most intriguing and fundamental concepts in quantum mechanics. It refers to the ability of particles, such as photons and electrons, to exhibit both wave-like and particle-like properties. The photoelectric effect, in particular, highlights this duality. Here, light is shown to knock electrons out of a metal surface, which suggests that light behaves like a particle with a quantifiable amount of energy.

However, light also behaves as an electromagnetic wave, exhibiting phenomena such as interference and diffraction. This duality is reconciled in quantum mechanics, which shows that the behavior of tiny particles is different from everyday objects: they don't fit neatly into the categories of 'particle' or 'wave' that we see in the macroscopic world.

The concept of wave-particle duality is best portrayed using experiments like the Double Slit Experiment, which show that particles can display interference patterns, a characteristic of waves, and yet be detected as discrete packets, indicating their particle nature. This contradictory nature questions our classical understanding of physics and has led to a deeper exploration into the foundations of reality.

Planck's constant, denoted as \( h \), is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. Introduced by Max Planck in 1900, this constant is the cornerstone of quantum theory, setting the scale of the quantum of action in the micro-world. The exact value of Planck's constant is \( 6.62607015 \times 10^{-34} \) joule-seconds.

Through the equation \( E = hu \), Planck's constant links the energy (\( E \)) of quantum events to the frequency (\( u \)) of the corresponding wave. The introduction of this constant led to the understanding that energy can only be emitted or absorbed in discrete 'chunks', or quanta, a concept that was revolutionary at the time and contradicted the prevailing wave theory of light.

In the photoelectric effect, Planck's constant is used to calculate the energy of the photons hitting the metal surface. If the photon energy exceeds the material's work function, an electron is emitted, demonstrating energy quantization. This realization not only gave insight into the nature of light but also laid the groundwork for the entire quantum mechanics field.