Planck’s constant (denoted by h) is a fundamental physical constant that plays a pivotal role in quantum mechanics. It is named after the German physicist Max Planck, who introduced it in 1900 while attempting to explain the observed spectrum of blackbody radiation. The value of Planck’s constant is approximately equal to 6.62607015 × 10^-34 joule-seconds (J·s) or 4.135667662 × 10^-15 electron-volts second (eV·s).

Planck’s constant sets the scale at which quantum mechanical effects become significant. It is central to several equations in quantum physics, including:

1. Quantization of Energy: The energy of a photon (particle of light) is given by E = hv, where E is the energy, v is the frequency of the light, and h is Planck’s constant. This equation shows that energy is quantized and can only exist in discrete packets or quanta.
2. Heisenberg Uncertainty Principle: The product of the uncertainty in a particle’s position (Δx) and the uncertainty in its momentum (Δp) must be greater than or equal to half of Planck’s constant divided by 2π: Δx * Δp ≥ ħ/2, where ħ is the reduced Planck constant, which is just Planck’s constant divided by 2π. This principle defines the inherent indeterminacy of particles in the quantum realm.
3. Schrödinger Equation: Planck’s constant appears in the Schrödinger equation, which describes the wave-like behavior of particles and governs the evolution of their quantum states.
4. Wave-particle Duality: The duality of particles having both wave and particle properties is defined in terms of Planck’s constant, with the wavelength of a particle given by λ = h/p, where p is its momentum.

As for why the universe depends on Planck’s constant, it’s because this constant determines the boundary between classical and quantum physics. Quantum mechanics, which is built upon Planck’s constant, explains the behavior of matter and energy at the atomic and subatomic levels, which ultimately governs the structure and dynamics of atoms, molecules, and all forms of matter in the universe. From the stability of atoms and the properties of materials to the workings of electronic devices and nuclear reactions, numerous aspects of the universe are fundamentally influenced by the value of Planck’s constant.