Calculate the density of flourine nucleus supposing that the shape of the nucleus is spherical and its radius is `5 xx 10^(-13)`. (Mass of `F`=`19` amu)

Options

A. `6.02xx10^(3) g " cm"^(-3)`
B. `5xx10^(4) g " cm"^(-3)`
C. `6.02xx10^(3) g " cm"^(-3)`
D. `5xx10^(13) g " cm"^(-3)`

Answer

C

Explanation

Radius of nucleus of F atom `=5xx10^(-13) " cm"`
Volume of sphere `=4//3pir^(3)=4//3xx22//7(5xx10^(-13)" cm")^(3)`
Mass of `6.023xx10^(23)` atoms of F (or their nuclei)=19g
Mass a 1 atom or 1 nucleus `=19//6.023xx10^(23)g`
Density of matter in F nucleus `=("Mass of nucleus")/("Volume of nucleus")`
`=((19g)xx3xx7)/((6.023xx10^(23))xx4xx22xx(5xx10^(-13)" cm")^(3))`
`=6.02xx10^(13)g " cm"^(-3)`