a) For a nucleus of , estimate very roughly how many nucleons would be at the surface.
b) If the binding energy of an interior nucleon due to the internucleon attraction were and if all nucleon were are tightly bound, the total binding energy would be . Taking into account the different binding of surface nucleons, roughly what would be the total binding energy?
a) The number of nucleons at the surface of the nucleus is roughly .
b) The total binding energy of nucleus is approximate .
Atomic number of nucleus, .
Radius of nucleons, is .
Binding energy of interior nucleon is .
Binding energy of surface nucleon is .
Area of the nucleus is given as:
Where, is the radius of large sphere, is the radius of nucleon.
The area contribution of each nucleon present on the boundary surface is where, .
Surface area of the nucleus is given as:
The number of nucleon present on the surface as shown below.
Substitute the values of area of nucleus in the above equation.
The total number of nucleons in the interior of the nucleus is .
Binding energy of each interior nucleon is and each surface nucleon contributes about half as much binding energy, that is .
The total binding energy would be given as follows:
Binding energy .
MRI relies on only a tiny majority of the nuclear magnetic moments aligning with the external field. Consider the common target nucleus hydrogen. The difference between the aligned and anti aligned states of a dipole in a magnetic field is Equation (8-7) can be used to find for the proton. Provided that the correct mass and gyromagnetic ratio are inserted. Using the Boltzmann distribution, show that for a field and a reasonable temperature, the number aligned exceeds the number anti aligned by less than .
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