Gamow's Theory of Alpha Decay AND Geiger Nuttal Law

Gamow's Theory of Alpha Decay gives and explanation as to how an alpha particle escapes the potential barrier of a nuclei even though its Kinetic Energy is less than the maximum potential height.

Its is a very interesting thing that vast majority of alpha particles have a maximum energy of around 4-9 MeV while the nuclear potentials of such nuclear species have a maximum of height of around 25MeV. How is it possible that such an alpha particle having kinetic energy 16-21 MeV less than the barrier potential still manages to escape from it. This is not allowed in Classical Physics. However, it is possible in Quantum Physics. Small particles having energy less than the barrier potential have a small but finite probability of 'tunneling' through that barrier. This is known as Quantum Tunneling.

George Gamow applied this concept of Quantum Tunneling to explain the above puzzle related to Alpha Decay.

One prediction of this theory is how two different alpha particles having different Kinetic Energies will show different barrier. Since tunneling probability depends on the width of the barrier, two different alpha particles having different Kinetic energies will experience two different 'effective' barriers. This will result in the fact that the half lives of both nuclear species will be different. As it turns out, the half life of a nuclear species that emits a high energetic alpha particle is less than the half life of a nuclear species that emits a low energetic alpha particle. This is the essence of Geiger Nuttal law, which has experimental validation.

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[FortheLoveofPhysics]

Q-Value (Kinematics) & KE of Alpha particle :
Beta Decay & Neutrino Hypothesis

[AditiShahaniMPH]

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[goutham]

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[dorotaaa]

I spent so much time looking for an answer what's the relationship between these two theories. This is the clearest explanation and now it seems so easy to understand. Thank you so much!

[Memorise]

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[CEO_of_Physics]

This Video is just perfect! I did not understand it at all from the university notes. Due to this video now I finally get where the Geiger-Natell law comes from an what it actually means!

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[ujjawalkumarsingh]

Thank you sir for having such a crystal clear concept of quantum tunneling in a very lucid manner

[prithvirajdj]

Very concisely explained. Helpful video.

Just a correction at some points in the end that the half-life being talked about is of the nucleus & not the @-particle.

The Geiger-Nuttal Law can also be written as:
ln ¥= B1 ln E + B2,
where ¥= decay constant (lambda),
B1 & B2 are constants for different series of transmissions.

[TheChalarock]

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[lofiburrito]

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[a.s.]

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[rajithayadav]

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