Question

An electron beam and a photon beam pass through identical slits. On a distant screen, the first dark fringe occurs at the same angle for both of the beams. The electron speeds are much slower than that of light. What can be concluded from this?

1) The wavelength of the electron beam is shorter than that of the photon beam.
2) The wavelength of the electron beam is longer than that of the photon beam.
3) The wavelength of the electron beam is equal to that of the photon beam.
4) The wavelength of the electron beam cannot be determined.

Answer 1

The dark fringe occurring at the same angle for both the electron beam and photon beam indicates that their wavelengths are equal as per the equation for double-slit interference.

Step-by-step explanation:

If an electron beam and a photon beam pass through identical slits and create the first dark fringe at the same angle on a distant screen, we can conclude that their wavelengths are identical. Since the equation d sin θ = mλ holds for both the electron beam and the photon beam, where d is the slit separation, θ is the angle of the dark fringe, m is the fringe order, and λ is the wavelength, the fact that the dark fringes occur at the same angle (θ) means that the wavelength (λ) of both beams must be the same for the observed m. Therefore, the correct conclusion is 3) The wavelength of the electron beam is equal to that of the photon beam.