The Compton wavelength and the Schwarzschild radius are two important quantities in physics that arise in different contexts.
- Compton wavelength: The Compton wavelength, denoted by λc, is a fundamental constant in quantum mechanics that relates the wavelength of a particle to its mass. It is named after Arthur H. Compton, who discovered the phenomenon of Compton scattering. The Compton wavelength is given by the formula:
λc = h / (mc)
Where h is the reduced Planck constant (approximately 6.62607015 × 10^(-34) J·s), m is the mass of the particle, and c is the speed of light (approximately 2.998 × 10^8 m/s). The Compton wavelength characterizes the quantum nature of a particle and provides a measure of the particle's wave-particle duality. It represents the scale at which the particle's wave-like behavior becomes significant.
- Schwarzschild radius: The Schwarzschild radius, denoted by Rs, is a concept from general relativity that defines the radius of a black hole or a spherical object with a given mass. It is named after Karl Schwarzschild, who derived the first exact solution to Einstein's field equations describing a non-rotating black hole. The Schwarzschild radius is given by the formula:
Rs = (2GM) / c^2
Where G is the gravitational constant (approximately 6.67430 × 10^(-11) m^3·kg^(-1)·s^(-2)) and M is the mass of the object. The Schwarzschild radius determines the size at which the object's gravitational pull becomes so strong that even light cannot escape from its surface. It defines the event horizon of a black hole, beyond which no information or particles can be observed from outside.
It's worth noting that the Compton wavelength and Schwarzschild radius are associated with different physical phenomena and have different applications in quantum mechanics and general relativity, respectively.