Does Quantum Tunnelling violate Heisenberg's Uncertainty principle??

I was recently watching a video by the channel Minute Physics, about the effect of quantum tunnelling and it's characteristics. In the video, the presenter told that quantum tunnelling refers to the state of probability of a sub-atomic particle to be in a place it is not supposed to be.

For example, if a ball is rolled down a cliff, in the classical world, there is no chance that the ball will cross the height, where it is thrown form. But, in the quantum world, there is a chance that if a sub atomic particle undergoes the same experiment, it might cross the hill, and there is also a minute chance of the particle being present in the hill.

It was further told that this creates a possibility of an electron been found in the nucleus, along with the protons and the neutrons. But, clearly, according to Heisenberg, this is not possible, as this would cause the speed of electron to be over the speed of light??

https://www.youtube.com/watch?v=cTodS8hkSDg --> This is the link to the video, and I would like for someone to correct me, if wrong, in the explanation of this video, or explain me the phenomenon behind this observation. Thanks!!

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Comments

Why would the velocity of the electron be over the speed of light if it is situated in the nucleus?

Steven Zheng - 6 years, 3 months ago

(dx)*(dv)>=h/4pi.....if dx is less than radius of nucleus....dv is greater than speed of light....am I ryt@abhineet nayyar

Mayank Shrivastava - 6 years, 3 months ago

First of all, the Heisenberg Uncertainty Principal states $\Delta x \Delta p \ge \frac{h}{4\pi}$ . These deltas mean the uncertainty (in the statistics sense); not a specific value of velocity or momentum.

@Steven Zheng – Yes!! I know that it's true that we consider the uncertainties. But, clearly how can the uncertainty in a measurement be more than the true value???

My hypothesis is that when an electrons enters the nucleus, it doesn't just stay there but combines with a proton to form a neutron and release a neutrino..Is this possible???

A Former Brilliant Member - 6 years, 3 months ago

@A Former Brilliant Member – That is possible. It is called electron capture, and is in fact responsible for most beta decay.

Also, the uncertainty just tells us that we cannot pinpoint the velocity of the particle when we measure it. We can measure the speed of the car at any given "resolution" of space to very precise accuracy. So for your electron case, we can't measure its speed to any accuracy given that we know very well where the electron is located in space. Also, you should think about the electron as a wavefunction that exists throughout all space, so $\Delta x$ with respect to where the electron is probably found should be greater than 1 angstrom.

@Steven Zheng – But then, why isn't it possible to cause quantum tunnelling on Earth?? I'm basically studying this for energy creation...

@A Former Brilliant Member – At what scale on Earth? Rocks in the video you presented will not tunnel. That was just an analogy. Pretty much only subatomic particles to small molecules tunnel effectively provided that they have sufficient energy or if the barrier it is tunnelling through is thin.

@Steven Zheng – Not the rocks! I mean is it possible to create a Mini-Sun on Earth, by Hydrogen-Helium conversion?

@A Former Brilliant Member – So you were talking about nuclear fusion! That is a complicated process and should be another discussion not related to HUP. there is a reason why we haven't achieved cold fusion. This is due to the fact that we need to add more energy to bind the two nuclei; hence, we are using energy, not producing. Although the release of energy is greater, we cannot contain it like a working energy plant.

@Steven Zheng – YESS!! But, then how is the sun doing it?? By raising it's temperature, to a large extent, right???

@A Former Brilliant Member – It begins with the gravitational interactions of gigantic gas clouds in space. The temperature and pressure is extremely high (more than anything we can achieve).

@Steven Zheng – That is the creation of Sun. See, i'm not interested in making the Sun. What I picture is the creation of that much Energy, without using that much. Scientist have wasted too much energy to create a Sun. But, what if we don't need a Sun??

@A Former Brilliant Member – I think we will be all dead! If you heard of the Kardashev scale, we are a TYPE 0 civilization. What you are trying to say is how can we be a TYPE 3 civilization. click here

@Steven Zheng – Ohkay! So, so maybe, we won't be able to use this type of energy in a go. But, this could be a lifelong power source!! See, in LHC, during the particle smashing, a temperature in about trillions is achieved easily, which is much more than the temperature at the Sun's core!

@A Former Brilliant Member – I don't think the temperature is 1 trillion K.

@Steven Zheng – Read this link : http://www.fromquarkstoquasars.com/what-is-the-highest-known-temperature/

The second para!!

@Steven Zheng – yes @Steven Zheng if uncertainity crosses speed of light....actual velocity needs to be greater than that... oh yeah....i made a mistake in typing... m not acquainted wid latex....so thats why

Yea...That's right @Mayank Srivastava !

http://www.reuters.com/article/2010/02/15/us-physics-temperature-idUSTRE61E3OB20100215 @Abhineet Nayyar You were right. Here's a more comprehensive resource.

Sanchit Ahuja - 6 years, 3 months ago

Bt I think what you say will be correct if the electron were to be in the nucleus all the time.... bt it is free to move moreover if u see the radial probability distribution of 1s orbital.....u ll see that it tends to infinity in the nucleus...

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$