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Answer: (a) Assuming nuclei are spherical in shape, show
Chapter 2, Problem 106P(choose chapter or problem)
(a) Assuming nuclei are spherical in shape, show that its radius \(r\) is proportional to the cube root of mass number (\(A\)).
(b) In general, the radius of a nucleus is given by \(r=r_{0} A^{1 / 3}\), where \(r_{0}\) is a proportionality constant given by \(1.2\times10^{-15}\mathrm{\ m}\). Calculate the volume of the \({ }_{3}^{7} \mathrm{Li}\) nucleus.
(c) Given that the radius of a \(\mathrm{Li}\) atom is 152 pm, calculate the fraction of the atom's volume occupied by the nucleus. Does your result support Rutherford's model of an atom?
Questions & Answers
QUESTION:
(a) Assuming nuclei are spherical in shape, show that its radius \(r\) is proportional to the cube root of mass number (\(A\)).
(b) In general, the radius of a nucleus is given by \(r=r_{0} A^{1 / 3}\), where \(r_{0}\) is a proportionality constant given by \(1.2\times10^{-15}\mathrm{\ m}\). Calculate the volume of the \({ }_{3}^{7} \mathrm{Li}\) nucleus.
(c) Given that the radius of a \(\mathrm{Li}\) atom is 152 pm, calculate the fraction of the atom's volume occupied by the nucleus. Does your result support Rutherford's model of an atom?
ANSWER:Step 1 of 4
We are assuming that the nucleus is spherical in shape. The formula for the volume of a sphere is:
\(\mathrm{V}=\frac{4}{3} \pi r^{3}\)