Nuclear Alchemy: The Transmutation of one Element into Another

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Nuclear Alchemy: The Transmutation of one Element into Another

I bombard aluminum 27 (13 protons and 14 neutrons), the stable type we have all come to know and love, with energetic alpha particles (two protons and two neutrons) at an energy of 5.3042 MeV! (MeV means Millions of Electron Volts). Most of the alpha particles would have bounced off of the aluminum without joining… but some would. Those lucky alpha particles bonded with the nucleus of the aluminum 27 to produce a new element: phosphorus 30! (15 protons and 15 neutrons). The reaction emits one spare neutron with way too much energy! =(

The phosphorus 30 has a short half-life of a mere 2.49 minutes, decaying into stable silicon 30 (14 protons and 16 neutrons) via beta+ decay (a positron). The position emitted is an Anti-Electon! That’s right, anti-matter. The quick little positron has an average energy of about 1438 keV (a max of 3203.3!!!). The position lasts only a short time before slamming into a normal electron and annihilating with an energy of 1022 keV, expressed as two gamma rays, each with 511 keV of energy. It is these emissions which I detect, using gamma spectroscopy. A Geiger counter would never be able to give me these results.

Al-27 + He-4 → P-30 + N
(e+) + e → y

I had calculated the energy of the reaction many times, but each calculation was a little wrong. I asked a very smart physicist for some help and he gave me a formula for figuring it out, but my math and his still didn’t add up…

Here is what I used for my determination:
I took the mass of an atom of P-30
(4.97802×10^-26 kg), call it M, and the mass of a single Neutron (1.67493×10^-27 kg), call it N, and the energy of the alpha particle which slammed into the aluminum (which was not at rest, but probably not doing too much whilst in its lattice, 5304.2 keV = 8.498×10^-13 joules, call it E. Also, let Em = momentum of P-30 atom after ejection of neutron, En momentum of neutron after being ejected: Em = (N/(M+N))E =(1.67493×10^-27 kg / (4.97802×10^-26 kg+1.67493×10^-27 kg)) 8.498×10^-13 j = 2.76620721*10^-14 joules = 172.6531 keV En = (M/(M+N))E = (4.97802×10^-26 kg /(4.97802×10^-26 kg+1.67493×10^-27 kg)^-1) 8.498×10^-13 j =8.22137928×10^-13 joules = 5.131382 meV

But… his numbers didn’t match (he thought the neutron would be 2.574 MeV and the phosphorus 30 would be 0.086 Mev.

Either way… OMG! That’s too much neutron flux for me in my tiny home lab. =)

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