Question

What are the odds of me experiencing Quantum Tunneling?

Asked by: Matt

Answer

The short answer is very very low. For the long, ugly answer, read on.

The probability of an object tunneling through a barrier as predicted by the Schrodinger equation can be found by the equation

P= e(-2KL)

Where L is the width of the barrier and K is the wave number, which is equal to [sqrt(2m(V-E))]/h

Where m is the mass of the object that we want to tunnel, V is the potential energy of the barrier, E is the energy of the tunneling object (usually kinetic), and h is Plank's Constant divided by 2*pi (approximately 1.06x10-34 J*s)

So let's take a look at all the above, since the exponent of the probability function is proportional to mass and barrier length, we can see that the probability of tunneling decreases exponentially as you increase mass and barrier length.

So, if you were 50kg, and were attempting to tunnel through a 30 joule potential barrier (equivalent to you trying to toss a 1kg object 3 meters in the air) which was 1 m wide, while running at 1m/s, the probability of you tunneling through would be approximately equal to:

P= e(-2((sqrt(100(30-25)))/h)(1)) = e(-4.219x10^35)

... which is so small it is almost zero. So once again, for a human being the answer is: almost impossible. However for objects with extremely small masses (such as electrons) the probability can be quite high.

Answered by: Loren Chang, Physics Undergrad, UC Irvine

Search

Loading



Sponsors

USC University of Southern California Dornsife College Physics and Astronomy Department McMaster University Physics and Astronomy Department

Science Quote

'There are two ways to live your life. One is as though nothing is a miracle. The other is as though everything is a miracle.'

Albert Einstein
(1879-1955)

Deal of the Day

Image of Hover Craft Kit. Click on this image for more info. Hover Craft Kit
Regular Price: $29.99
Today's Price: $12.00
Learn the science behind hover craft technology with this cool kit! Buy it now! Deal ends at midnight!

Top Selling

Here are our physics & astronomy bestsellers:
Mini Plasma Ball
Slide Making Kit
Top Secret - Spinning Top
Wood Grain Newtons Cradle
Deluxe 3D Mirascope
Solar Radiometer
Periscope
Ultimate Chemistry Set CHEM C3000
Solar Science 4M Kit
3D Magnetic Field Tube