An atomic radii is difficult to quantify because electrons move towards and away from the nucleus (in electron clouds). The nucleus also does not have a defined boundary, but the radius can be approximated by the following value:
\(1\) femtometer is equivalent to \(10^{-15}\) meters.
Thus, the volume of the sphere increases proportionally to the atomic mass. The ratio \( V/A\) is also constant suggesting the density is uniform like a liquid drop (i.e. the liquid-drop model).
The radius of an unknown nucleus is determined to be twice a large as another. What is the ratio of their masses?
The first element can be expressed as:
\(R_1 = 1.25 \cdot A^{1/3}_1\)
The second element can be expressed as:
\(R_2 = 1.25 \cdot A^{1/3}_2\)
The second radius is twice the first:
\(R_2 = 2 \cdot R_1\)
We can substitute the respective values to determine the ratio of the masses:
\(1.25 \cdot A^{1/3}_2 = 2 \cdot 1.25 \cdot A^{1/3}_1\)
\(A^{\frac{1}{3}}_2 = 2 \cdot A^{1/3}_1\)
\(A_2 = 8 \cdot A_1\)
\(\cfrac{A_2}{A_1} = 8\)
Thus, the mass of the unknown element is \(\boldsymbol{8}\) times larger than the known element.