5) A rough estimate of the radius of a nucleus is provided by the formula r= kA ^1/3, where k is approximately 1.3 X 10^-13 cm and A is the mass number of the nucleus. Estimate the density of the nucleus of I-129 (which has an exact nuclear mass of 2.15994 X 10-22 g) in grams per cubic centimetre. Compare with the density of solid Iodine, 4.93 g cm-1.

Question

5)	A rough estimate of the radius of a nucleus is provided by the formula r= kA ^1/3, where k is approximately 1.3 X 10^-13 cm and A is the mass number of the nucleus.  Estimate the density of the nucleus of I-129 (which has an exact nuclear mass of 2.15994 X 10-22 g) in grams per cubic centimetre.  Compare with the density of solid Iodine, 4.93 g cm-1.

aaronq · Answer

It's asking you to find the estimate the density of I-129.

$\sf density=\dfrac{mass}{Volume}$

the mass is given in the question (no need to convert units already in grams)

the volume of a sphere is $\sf V=\dfrac{4}{3}\pi r^3$, the radius is approximated with $\sf r=kA^{\frac{1}{3}}$, so the density is:

$\sf density=\dfrac{m}{\dfrac{4}{3}\pi (kA^{\frac{1}{3}})^3}=\dfrac{3}{4\pi}\dfrac{2.15994*10^{-22}g}{(1.3 * 10^{-13} cm)^3*(129)}$