Answer to Question #218281 in Physical Chemistry for Mariam

Question

Assuming that the atomic nucleus is spherical, calculate the volume of the nucleus given that it's radius is 10^-5 that of the atom with radius 10^-10m.

Answer 1

The volume of the nucleus will be

$V_ {nucleus} = \frac{4} 3 π ⋅ ( 10^ {− 5} )^3 cm^ 3$

The volume of the atom will be

$V_ {atom} = \frac{4} 3 π ⋅ ( 10^{ − 10} )^3 . cm 3$

Divide the two volumes to get the fraction of the atom occupied by the nucleus

F

$\frac{V_{nucleus}}{V_{atom}}=\frac{\frac{4}{3}π(10^{-5})^3} {\frac{4}{3}π(10^{-10})^3}=[\frac{10^{-5}}{10^{-10}}]^3=1.0×10^{15}$

This means that the nucleus occupies $1.0×10^{15}$  of the volume of the atom.