Question

A beam of photons with wavelength 150 nm and beam of electrons having the same energy as the photons go through the same slit of width 355 nm. You observe the diffraction pattern on a distant screen. All angles are measured from the centerline. The photons produce their first dark band at an angle α. Is the magnitude of α bigger than, equal to, or smaller than the magnitude the angle, β, where the electrons produce their first dark band?

Answer 1

Answer:

Explanation:

For moving particle , the wavelength is given by the expression

$\lambda=\frac{h}{\sqrt{2mE} }$

E is kinetic energy of the particle

Here particle is electron and its kinetic energy

E = 150 nm

= 1244 / 150

= 8.3 eV

8.3 X 1.6 X 10⁻¹⁹ J

=13.28 X 10⁻¹⁹ J

Putting these values in the expression for wavelength as given above we have

$\lambda=\frac{6.6\times10^{-34}}{\sqrt{2\times9.1\times10^{-31}\times13.28\times10^{-19}} }$

λ = .425 nm

Wave length of electron wave will be 0.425 nm

Hence its wavelength will be smaller and therefore magnitude of angle made by it will also be smaller. So magnitude of β will be smaller than that of α .