Do atoms really exist?

To "see" an object with a light microscope means to be able to resolve light that scatters from different parts of the object. If in the view of your microscope, it appears that all light from an object is a blur, it means the object's fine details are below your limit of detection. As it turns out, it is the wavelength of the incident photons that determines the length scale at which details begin to merge into a blur.

There are several seemingly plausible arguments that suggest long wavelength light would be better for imaging small details, but it is actually the other way around. If you want to image small details, you need shorter and shorter wavelengths of incident radiation, but why is this?

The simplest explanation actually comes from the Heisenberg uncertainty principle. Recall, the uncertainty principle says that we cannot simultaneously know the position and momentum of a particle along a spatial dimension below some minimum level of uncertainty. If we write our uncertainty in position as $\Delta x$ and our uncertainty in its momentum as $\Delta p_x$ , then we have

$\Delta x \Delta p_x \geq h/4\pi$

Now, if the feature we're resolving has length scale $L$ , we need $\Delta x$ of order at most $L$ . When the photon scatters off our feature it will hit the detector somewhere in a distribution (the black distribution shown below). This cause of this distribution is our uncertainty in the momentum of the photon in the $x$ direction after it scatters. Before the photon hits the donut, we know it has momentum purely in the $y$ direction, but after the scatter, all we know is that it ended up somewhere in the black distribution. If it has zero momentum in the $x$ direction, it will end up at the center of this distribution. It can also have momentum in the $x$ direction as large as $p\sin\theta$ and still hit the edge of the black distribution. Thus, our uncertainty in $x$ -momentum is $\Delta p_x \approx p\sin\theta$ .

Note, it might seem as if there is no problem, if the particle hits a particular position at the detector, it must have come from a specific location. The key is, every position on the donut has some characteristic distribution, and these all overlap. Thus we can never know for sure where a particle came from, only a region where it could have plausibly come from. If the features in the object change appreciably over a much shorter length scale than our uncertainty in position, the image will be blurred.

Thus, we have

$\begin{aligned} \Delta x \Delta p_x &\geq h/4\pi \\ Lp\sin\theta &\geq h/4\pi \end{aligned}$

However, the momentum of a photon is given by $p = h/\lambda$ , thus

$\frac{L\sin\theta}{\lambda} \sim 1/4\pi$

and thus $L\sim\lambda$ , showing that the length scale of our microscope's resolution is on the scale of the wavelength of our incident radiation, in this case, visible photons. Since the visible spectrum has wavelengths in the hundred-nanometer range, we should expect to see our images blur at the hundred-nanometer scale, or about at the scale of viruses. This means we will not be able to see anything smaller such as proteins, DNA, small molecules, or atoms using a light microscope.

In order to make progress, we need to use radiation of wavelength comparable to the object of interest. Electrons have wavelength much shorter than the photon (about 1 nm) and are therefore good choices to resolve proteins and perhaps small molecules. Recent progress has brought electron microscopy nearly to the atomic scale.

There are other ways of bypassing these limits. For instance, imaging the same object for a very long time, one can drive the signal well above the noise so as to obtain final images much more finely resolved than any of the component measurements.

Any object can be visualized only when the light rays from some source bounce back from the object and fall on our eyes. The image captured on our retina is sent to our brain and is understood by it.

But the image can be captured only if the light rays bounce back. If this should happen, the light rays should be smaller than the object . But if the object is smaller than the light ray itself how can we expect it to bounce back?

Which is why atoms are not perceivable to us. They are smaller than the smallest wavelength of a light . When we direct a light ray on it, we can't receive a clear image.