An element X is written as:

^{A}_{Z}X,

where A is the nucleon number and Z is the atomic number.

Approximate radius:

$\overline{){\mathbf{R}}{\mathbf{=}}{{\mathbf{R}}}_{{\mathbf{0}}}{{\mathbf{A}}}^{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{3}$}\right.}}$

Density:

$\overline{){\mathbf{\rho}}{\mathbf{=}}\frac{\mathbf{m}}{\mathbf{V}}}$

It has been found that the radii of most nuclei are well approximated by the equation *R*=*R*_{0}*A*^{1/3}, where *R*0=1.2x10^{-}^{15} m is an experimentally determined constant. Because the mass of a nucleon (a proton or a neutron) is close to one atomic mass unit (1u), the nucleon number *A* is sometimes called the mass number.

**Part A**

What is the approximate radius *R* of ^{208}_{82}Pb?

Express your answer in meters to two significant figures.

R = ____ m

**Part B**

Assuming that each nucleus is roughly spherical and that its mass is roughly equal to *A* (in atomic mass units u), what is the density ρ of a nucleus with nucleon number *A*?

Express your answer in terms of *A*, *R*_{0}, and π.

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