Answer:
The diameter is [tex]d = 8.18*10^{-19} \ m[/tex]
Explanation:
From the question we are told that
The value of one atomic mass unit is [tex]u = 1.66 *10^{-27} \ kg[/tex]
The density of the proton is [tex]\rho = 5.8 *10^{27} \ kg/m^3[/tex]
Generally the volume of the proton (sphere)is mathematically represented as
[tex]V = \frac{4}{3} * \pi * r^3[/tex]
Generally this volume can also be evaluated as
[tex]V = \frac{u}{\rho}[/tex]
=> [tex]V = \frac{1.66 *10^{-27}}{5.8*10^{27}}[/tex]
=> [tex]V = 2.862 *10^{-55} \ m^3[/tex]
So
[tex]2.862 *10^{-55} = \frac{4}{3} * 3.142 * r^3[/tex]
=> [tex]r^3 = 6.832 *10^{-56}[/tex]
=> [tex]r = 4.088 *10^{-19} \ m[/tex]
Now the diameter is mathematically represented as
[tex]d = 2 * r[/tex]
=> [tex]d = 2 * 4.088 *10^{-19}[/tex]
=> [tex]d = 8.18*10^{-19} \ m[/tex]
