The graph of ln left(frac{R}{R_0}right) versu | vedclass

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(A) The relationship between the radius $R$ of a nucleus and its mass number $A$ is given by the formula:$R = R_0 A^{1/3} \dots(1)$Taking the natural

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$A$ straight line

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(A) The relationship between the radius $R$ of a nucleus and its mass number $A$ is given by the formula:$R = R_0 A^{1/3} \dots(1)$Taking the natural logarithm on both sides:$\ln(R) = \ln(R_0 A^{1/3}) = \ln(R_0) + \frac{1}{3} \ln(A)$Rearranging the terms to isolate the ratio:$\ln(R) - \ln(R_0) = \frac{1}{3} \ln(A)$$\ln \left(\frac{R}{R_0}\right) = \frac{1}{3} \ln(A)$This equation is of the form $y = mx$,where $y = \ln \left(\frac{R}{R_0}\right)$,$x = \ln(A)$,and the slope $m = \frac{1}{3}$.Since this represents a linear equation passing through the origin,the graph is a straight line.

The graph of $\ln \left(\frac{R}{R_0}\right)$ versus $\ln A$ is,where $R$ is the radius of a nucleus,$A$ is its mass number,and $R_0$ is a constant.

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