The relationship to calculate the wavelength of electromagnetic radiation (EMR) and electrons depends on their respective properties and behaviors.
For Electromagnetic Radiation (EMR): The wavelength of electromagnetic radiation can be determined using the following equation:
Wavelength (λ) = speed of light (c) / frequency (f)
Here, the speed of light (c) is a constant value equal to approximately 299,792,458 meters per second in a vacuum. The frequency (f) represents the number of wave cycles per second and is measured in hertz (Hz).
For example, if you have the frequency of an electromagnetic wave, you can calculate its wavelength by dividing the speed of light by the frequency.
For Electrons: The wavelength of electrons is governed by the de Broglie wavelength equation, which is based on wave-particle duality. According to this equation:
Wavelength (λ) = Planck's constant (h) / (mass (m) × velocity (v))
In this equation, Planck's constant (h) is a fundamental constant in quantum mechanics, approximately equal to 6.62607015 × 10^-34 joule-seconds. The mass (m) represents the mass of the electron, and the velocity (v) denotes the velocity of the electron.
This equation suggests that the wavelength of electrons is inversely proportional to their momentum (mass × velocity). As the velocity of an electron increases, its wavelength decreases, and vice versa. It implies that the behavior of electrons can exhibit wave-like characteristics, such as interference and diffraction.
It's important to note that the de Broglie wavelength equation is applicable to particles with wave-like properties, not just electrons. However, it is most commonly associated with electrons due to their relatively low mass and high speed in certain scenarios, making their wave-like behavior more noticeable.