Nuclear Radius

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Experiments show that the radius of an atomic nucleus depends on its mass number through R = R0 A^(1/3), with R0 = 1.2 fm. What is the approximate radius of a nucleus whose mass number is 125?

RankGuru · Accepted Answer

Scattering experiments establish that nuclear radius grows with mass number as $R = R_0 A^{1/3}$, where $R_0 = 1.2$ fm is an empirical constant; the cube-root dependence reflects that nuclear volume is proportional to the number of nucleons. For $A = 125$, the cube root is $A^{1/3} = 125^{1/3} = 5$, so $R = 1.2 	imes 5 = 6.0$ fm. The value 1.2 fm is simply $R_0$ and ignores the mass-number factor. The value 150 fm wrongly multiplies $R_0$ by $A$ itself instead of by $A^{1/3}$. The value 2.4 fm corresponds to $A = 8$ (cube root 2) and uses the wrong mass number. This matches the NCERT empirical nuclear-size relation. A plausibility check confirms the radius is of the order of a few femtometres, the correct scale for medium-mass nuclei, and grows much more slowly than the mass number, consistent with the cube-root law.

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