Question

The nucleus of an atom $X$ is supposed to be a sphere with a radius of $5\times {10}^{-13}cm$. Find the density of the matter in the atomic nucleus if the atomic weight of $X$ is 19.

• A. $=6.02\times {10}^{14}g/mL$
• B. $=64\times {10}^{13}g/mL$
• C. $=6.02\times {10}^{13}g/mL$
• D. $=6.02\times {10}^{-13}g/mL$

Answer 1

The correct option is C $=6.02\times {10}^{13}g/mL$

Radius $=5\times {10}^{13}cm$

Volume $=\frac{4}{3}\pi r^3=\frac{4}{3}\times 3.14\times (5\times {10}^{-13}{)}^3=5.2\times {10}^{-37}c{m}^3$

Mass of nucleus $=\frac{19}{6\times {10}^{23}}g=3.2\times {10}^{-23}g$

Density $=\frac{mass}{volume}$

$=\frac{3.2\times {10}^{-23}g}{5.2\times {10}^{-37}c{m}^3}=6.02\times {10}^{13}g/mL$