A graph is plotted between the natural logarithm of the nuclear radius ( R ) on the y-axis and the natural logarithm of the mass number ( A ) on the x-axis for various nuclei. The resulting graph is a straight line. The slope of this straight line is:

Step-by-step solution

The relation between the nuclear radius R and the mass number A is given by: R = R₀ A^ 1/3 Taking the natural logarithm on both sides, we get: R = R₀ + 1 3 A Comparing this equation with the standard equation of a straight line, y = mx + c , where y = R and x = A , we find: Slope ( m ) = 1 3 y-intercept ( c ) = R₀ Therefore, the slope of the graph is 1 3 . Answer: 1 3