Answer :
The width of the electron beam after traveling 10m is 122.7 mm.
The width of the electron beam after traveling 10m when a beam of 100ev electrons is sent through a single slit that is 1um wide.
Diffraction is the phenomenon of a wave, such as light or sound, spreading out when it encounters an obstacle or a slit with a size similar to its wavelength.
It is also known as Huygens-Fresnel principle.The formula to calculate the diffraction pattern of a single slit is given byd sin θ = λ,
where d is the width of the slit, θ is the angle between the incident light and the diffracted light, and λ is the wavelength of the light used.
In this case, we will consider electrons, so we need to use the de Broglie wavelength equation. The de Broglie wavelength (λ) of an object with mass (m) and velocity (v) is given byλ = h / mvwhere h is Planck's constant.
We can rewrite this equation asλ = 12.27 / √Ewhere E is the energy of the electron in eV. In this case, E = 100 eV, soλ = 12.27 / √100 = 1.227 nm.
Substitute the value of λ in the diffraction equation and solve for the angleθ = sin-1(λ/d)θ = sin-1(1.227 nm / 1000 nm) = 0.0721 rad.
To find the width of the beam after traveling 10 m, we need to use the formula for the diffraction pattern of a single slit, which is given byw = λL / dwhere L is the distance traveled by the beam.
In this case, L = 10 m and d = 1 µm = 10-6 m. Substituting the values, we get = (1.227 nm)(10 m) / (10-6 m) = 122.7 mmTherefore, the width of the electron beam after traveling 10m is 122.7 mm.
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