Which of the following is not an assumption involvedin the expression: r = (1.2

Question

Which of the following is not an assumption involvedin the expression: r = (1.2 ×10–15 m)A1/3?

a. All nucleons have roughly the samemass.
b. The number of nucleons isproportional to the nuclear mass.
c. Nuclei areincompressible.
d. The nucleus is spherical inshape.
e. Nuclear densities are proportional to the mass numbers. Which of the following is not an assumption involvedin the expression: r = (1.2 ×10–15 m)A1/3? All nucleons have roughly the samemass. The number of nucleons isproportional to the nuclear mass. Nuclei areincompressible. The nucleus is spherical inshape. Nuclear densities are proportional to the mass numbers.

Explanation / Answer

Since the time f rutherford's scattering experiments,amultitude of other experiments have shown that most nuclie areapproximately spherical and have an average radius given by r = ro * A1/3 ------------(1) where ro is a constant equal to 1.2 * 10-15 m and Ais the mass number.Because the volume of a sphere is proportionalto the cube of its radius,it follows from equation (1) that thevolume of a nucleus (assumed to be spherical) is directlyproportional to A,the total number of nucleons.This proportionalitysuggests that all nuclie have nearly the same density.When nucleonscombine to form a nucleus,they were tigtly packedspheres.Therefore,the assumption which is not involved in theexpression of equation (1) is all nucleons have roughly the samemass. where ro is a constant equal to 1.2 * 10-15 m and Ais the mass number.Because the volume of a sphere is proportionalto the cube of its radius,it follows from equation (1) that thevolume of a nucleus (assumed to be spherical) is directlyproportional to A,the total number of nucleons.This proportionalitysuggests that all nuclie have nearly the same density.When nucleonscombine to form a nucleus,they were tigtly packedspheres.Therefore,the assumption which is not involved in theexpression of equation (1) is all nucleons have roughly the samemass.

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