ParrotPete said:Homework Statement
Given an electron with total energy 1 KeV, determine it's deBroigle wavelength.
Homework Equations
E^2 = (mc^2)^2+(pc)^2
[tex]\lambda[/tex] = [tex]\frac{h}{p}[/tex]
The Attempt at a Solution
(pc)^2 = E^2 - (mc^2)^2 <> p = ± [tex]\frac{1}{c}[/tex] [tex]\sqrt{E^2-(mc^2)^2}[/tex]
What am I doing wrong?
When I plug in E = 10^3 eV and (mc^2) = 0.511 * 10^6 eV I get an imaginary result.
DeBroigle wavelength, also known as matter wavelength, is the characteristic wavelength associated with a particle, such as an electron, that exhibits wave-like behavior.
DeBroigle wavelength is directly related to the momentum of a charged electron. The higher the momentum, the shorter the deBroigle wavelength and vice versa.
The equation is given by λ = h/p, where λ is the deBroigle wavelength, h is the Planck's constant, and p is the momentum of the charged electron.
Knowing the deBroigle wavelength of a charged electron is important because it helps us understand the wave-particle duality of matter and has practical applications in various fields such as quantum mechanics and electron microscopy.
The deBroigle wavelength of a charged electron can be experimentally determined by using a diffraction grating or a double-slit experiment, where the interference pattern of the electron is measured and the wavelength is calculated using the equation mentioned above.