What is the range of size for quantum effect to happen?

[Tareq Naushad]

Please check the youtube video on sizes from Planck length to whole universe . My question is at 1:34 instance.


What is the range of the size for the quantum effects to happen at noticeable state i.e. as per the sizes shown in the video from which point upto which point we can expect the quantum nature of particles should occur? At 1:34 the sizes of UV light, virus, transistor gate are shown. Can I assume that transistor gate, virus etc. may face the quantum effects i.e. uncertainty, wave-particle duality etc.

 

[mfb]

There is no fixed size limit, it depends on the system. Some quantum effects have large macroscopic consequences, e. g. the fact that there are solids, or conductivity in metals, or superconductors. On the other hand, there are particles that you can treat classical, e. g. cosmic rays propagating through vacuum.

 

[jfizzix]

It is a relatively gradual transition.

At larger length scales, quantum effects can still be significant, but only in other limits, such as low temperature.

A good rule of thumb for the distance that quantum effects are significant is what's known as the thermal DeBroglie wavelength:

$\lambda_{th}\equiv\frac{h}{\sqrt{2\pi m k_{B}T}}$

Roughly speaking, it is the DeBroglie wavelength of a particle of mass $m$ and mean kinetic energy $\pi k_{B} T$, where $k_{B}$ is Boltzmann's constant, and $T$ is the temperature in Kelvins.

As an example, a helium atom cooled to 2 Kelvin will have a thermal DeBroglie wavelength of about 0.6 nanometers.
For reference, the typical radius of a helium atom is about 0.03 nanometers, so at 2 kelvin, the thermal DeBroglie wavelength is a lot larger than the typical size of the object itself.
Indeed, at these temperatures, quantum effects are very significant, as liquid helium is a superfluid at this temperature.

It's a good rule of thumb to say that when the thermal DeBroglie wavelength is larger than the size of the object itself, the quantum wave nature of the object will be important.

As an extra side note, the thermal DeBroglie wavelength for an electron in a transistor at room temperature is about 4.3 nm. With the latest generation of CPUs having transistors as small as 10-20 nm, it won't be long before quantum effects become an unavoidable source of complication when designing new computer hardware.
It is also at this "5nm" length scale that quantum tunneling has been calculated to limit the effectiveness of transistors. If electrons can just tunnel across the gap made by the transistor, then it simply cannot work in the same way that larger scale transistors are known to do.