The last element

I was just thinking what can be the last atomic number that can exist within the range of permissible radioactivity limit and considering all other factors in quantum physics and chemical factors.Can there be a limit to the number of elements that exist in nature?Can we go beyond something that is totally unimaginable?

Nobody really knows. Using the naive Bohr model of the atom, we run into trouble around Z=137 as the innermost electrons would have to be moving above the speed of light. This result is because the Bohr model doesn’t take into account relativity. Solving the Dirac equation, which comes from relativistic quantum mechanics, and taking into account that the nucleus is not a point particle, then there seems to be no real issue with arbitrarily high atomic numbers, although unusual effects start happening above Z≈173. These results may be overturned by an even deeper analysis with current quantum electrodynamics theory, or a new theory altogether.

Why 137? ’Nobody knows’, Feynman (one of the great physicist)admitted, adding that ’it’s one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the hand of God wrote that number, and we don’t know how He pushed his pencil.’ It’s one of the constants that must be added to fundamental physics by hand. Werner Heisenberg was convinced that the problems than plaguing quantum theory would not go away until 137 was ’explained’. But neither he nor Pauli nor anyone else has cracked the problem.

But was Feynman right about untriseptium? His argument hinged on the fact that a features in the solution of the Dirac equation for the ground-state energy of an atom’s 1s electrons. In effect, when the atomic number Z   is equal to or greater than 137 the energy becomes imaginary or, in other words, oscillatory – there is no longer a bound state. This doesn’t in itself actually mean that there can be no atoms with >137, but rather, there can be no neutral atoms.

However, Feynman’s argument was predicated on a Bohr-type atom in which the nucleus is a point charge. A more accurate prediction of the limiting Z  has to take the nucleus’s finite size into account, and the full calculation changes the picture. Now the energy of the 1s orbital doesn’t fall to zero until around Z   = 150; but actually that is in itself relatively trivial. Even though the bound-state energy becomes negative at larger Z , the 1s electrons remain localised around the nucleus.

But when Z  reaches around 173, things get complicated.1 The bound-state energy then dives into what is called the negative continuum: a vacuum ’sea’ of negative-energy electrons predicted by the Dirac equation. Then the 1s states mix with those in the continuum to create a bound ’resonance’ state – but the atom remains stable. If the atom’s 1s shell is already ionised, however, containing a single hole, then the consequences are more bizarre: the intense electric field of the nucleus is predicted to pull an electron spontaneously out of the negative continuum to fill it. In other words, an electron-positron pair is created and the electron plugs the gap in the 1s shell while the positron is emitted.

This behaviour was predicted in the 1970s by Burkhard Fricke of the University of Kassel, working with nuclear physicist Walter Greiner and others.1 Experiments were conducted during that and the following decade using ’pseudo-atoms’ – diatomic molecules of two heavy nuclei created in ion collisions – to see if analogous positron emission could be observed from the innermost molecular rather than atomic orbitals. It has been not yet known exactly what would happen for Z >173.

What you think about the last element?

Share your thoughts and theories.




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