when an alpha particle hit berrelyium it emits neutron. Does the alpha particle causes unstability to the nucleus or any other reason?
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The reaction can be regarded as a fusion reaction, the fast moving helium nucleous has sufficent energy to overcome the electrostatic repulsion of the positvely charged beyllium nuclous. What happens is that the alpha particle will enter the berylium nucleous to form the product.
The product will be carbon 13 in an excited state, the carbon 13 could relax down to the ground state by the emission of gamma rays (photons) but by the ejection of a neutron it is able to convert itself into the very stable carbon-12.
In the same way as in chemistry we have the chemcially very stable noble gases (full electron shells) in nuclear science we have some nuclides which are blessed with additional stability.
Carbon-12 has both an even number of protons and neutrons which will increase its stability more than a odd,odd, even,odd or odd,even nuclide. Also there are some magic numbers which correspond to complete shells of nucleons (protons and neutrons). Carbon-12 is not one of these magic nuclides (full shells of protons and/or neutrons) but it is more stable than carbon-13.