Question

A beam of electrons passes through two slits which are 10 μm apart. A CCD detector (similar
to that used in a digital camera) is sensitive to the arrival of electrons and is placed 1 m away
from the slits. The pixels of the CCD are square and are 1μm across. The following numbers
of electrons are recorded in adjacent detector cells: 12, 65, 95, 67, 13, 10, 70, 110, 68, 11,15,64, 90.
(iii) Explain why the data has this structure. (It may help to make a rough sketch of the data)
[1 mark]

(iv) What is the kinetic energy of the electrons in the beam (expressed in eV) ?
(You can assume they are not moving at relativistic speeds) [4 marks]
(v) If you threw tiny grains of sand through these slits, would you see a similar pattern?
Justify your answer.

Answer 1

iii) The data in this format indicates that this experiment is a version of Young's double slit experiment, where the wave nature of electrons play an important role to create a series of maxima and minima on the CCD screen which correspond to interference pattern.. The numbers precisely demonstrate the pattern 110 is a central maxima surrounded by two minimas with number 70 and 68. Again the secondary maxima is obtained at 95 and 90 respectively and so on.

iv) To calculate the kinetic energy of the electron, we need to find its wavelength.

So, the distance of nth maxima from the central maxima is given as,

Now, x = 5 um for n = 1, as the first maxima 95 is 5 detectors away from central maxima 110, each detector being 1 um.

D = 1m = 10⁶ um ; d = 10 um.

Therefore, wavelength is,

Momentum of the electron

Kinetic energy of the electron,

iv) For a similar interference pattern to be observed, the beams passing through the slits have to be coherent, for the sand grains, finding particles of exactly same mass is quiet impossible, hence no coherent source of light. So these pattern can not be observed with sand grains.