Question

Suppose an attractive nuclear forc eacts between two protons which may be written as $F=C\frac{e^{-kr}}{r^2}$ (a) Write down th edimensional formulae and appropriate SI unit of c and k. (b) supose that k = $1ferm{i}^{-1}$ 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.

Answer 1

(a) Given, $F=\frac{C{e}^{-kr}}{r^2}$
Since $e^{-kr}$ is pure number
So, $K=\frac{1}{r}=\left[L^{-1}\right]C=\left[M{L}^3{T}^{-2}\right]\left(b\right)F=\frac{9\times {10}^9\times (1.6\times {10}^{-19}{)}^2}{(5\times {10}^{-15}{)}^2}=\frac{C\times {10}^{-5}}{(5\times {10}^{-15}{)}^2}\therefore C=3.4\times {10}^{-26}N-m^2$