In an experiment, electrons are made to pass through a narrow slit of width 'd' comparable to their de Broglie wavelength. They are detected on a screen at a distance 'D' from the slit (see figure). Which of the following graphs can be expected to represent the number of electrons 'N' detected as a function of the detector position 'y'( y = 0 . corresponds to the middle of the slit . \, )

Dual Nature of Radiation PYQ — JEE Main 2008 · Shift 0 · Q61 with Solution

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Correct answer: D

Identify the physical situation

Electrons are passing through a single narrow slit of width $d$ , where $d$ is comparable to the electron de Broglie wavelength $\lambda$ .

Since electrons have wave nature, passing through a slit produces diffraction.
What pattern is expected on the screen?

For a single slit, the intensity distribution on the screen is of the form
$I(\theta) \propto \left(\frac{\sin \beta}{\beta}\right)^2, \qquad \beta = \frac{\pi d \sin\theta}{\lambda}$
The number of electrons detected at a point is proportional to this intensity:
$N(y) \propto I(y)$
Features of single-slit diffraction pattern

The graph of $N$ vs $y$ must therefore have:
- a central maximum at $y=0$
- symmetry about $y=0$
- side maxima of much smaller height on both sides
- minima in between
So the distribution is not uniform, and it is also not just two peaks. It is a diffraction envelope with one broad central peak and weaker side peaks.
Choose the correct graph

Among the given options, the graph representing a single-slit diffraction pattern is Option D.
Comparison with stored answer

My derived answer is D, which matches the stored correct answer.

View written solutionFree

Correct answer: D

Identify the physical situation

Electrons are passing through a single narrow slit of width $d$ , where $d$ is comparable to the electron de Broglie wavelength $\lambda$ .

Since electrons have wave nature, passing through a slit produces diffraction.
What pattern is expected on the screen?

For a single slit, the intensity distribution on the screen is of the form
$I(\theta) \propto \left(\frac{\sin \beta}{\beta}\right)^2, \qquad \beta = \frac{\pi d \sin\theta}{\lambda}$
The number of electrons detected at a point is proportional to this intensity:
$N(y) \propto I(y)$
Features of single-slit diffraction pattern

The graph of $N$ vs $y$ must therefore have:
- a central maximum at $y=0$
- symmetry about $y=0$
- side maxima of much smaller height on both sides
- minima in between
So the distribution is not uniform, and it is also not just two peaks. It is a diffraction envelope with one broad central peak and weaker side peaks.
Choose the correct graph

Among the given options, the graph representing a single-slit diffraction pattern is Option D.
Comparison with stored answer

My derived answer is D, which matches the stored correct answer.