# Problem: It has been found that the radii of most nuclei are well approximated by the equation R=R0A1/3, where R0=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 AWhat is the approximate radius R of 20882Pb?Express your answer in meters to two significant figures.R = ____ mPart BAssuming 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, R0, and π.

###### FREE Expert Solution

An element X is written as:

AZX,

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

$\overline{){\mathbf{R}}{\mathbf{=}}{{\mathbf{R}}}_{{\mathbf{0}}}{{\mathbf{A}}}^{\mathbf{1}}{\mathbf{3}}}}$

Density:

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

###### Problem Details

It has been found that the radii of most nuclei are well approximated by the equation R=R0A1/3, where R0=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 20882Pb?