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Suppose an attractive nuclear force acts between two protons which may be written as F = Ce-kr/r2. (a) Write down the dimensional formulae and appropriate SI units of C and k. (b) Suppose that k = 1 fermi-1 and that the repulsive electric force between the protons is just balanced by the attractive nuclear force when the separation is 5 fermi. Find the value of C.
Sol. Expression of electrical force F = C * e^-kr/r^2 Since e^-kr is a pure number. So, dimecsional formulae of F = dim ensional formulae of C/dim ensional formulae of r^2 Or, [MLT^–2][L^2] = dimensional formulae of C = [ML^3T^–2] Unit of C = unit of force × unit of r^2 = Newton × m^2 = Newton–m^2 Since –kr is a number hence dimensional formulae of K = 1/dim entional formulae of r = [L^-1] Unit of k = m^-1
Already in peat b given k=1Fermi-1so k is simply per meter *and since e is purely a number equate c to f*rsquare
For part b)equate F=kq1q2/r*2 to F=C/e*kr.r*2 then r*2 on both sides cancelled put value of e as 2.7 power 5 u will get the answer as 3.3*10power -26
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