Question

What is the likely mass number of a spherical nucleus with a radius of 3.6 fm as measured by electron-scattering methods?

Short answer

The likely mass number of the nucleus is 27.

Step-by-step solution

Given data

Radius of the nucleus, r = 3.6 fm

Understanding the concept of nuclear radius

The nuclear radius, R, can be defined as the distance from the center to the point where the density has decreased to half its original value. In calculation, the radius is directly proportional to the one-third power of the mass number of the nucleus.

Formula:

The radius of an atom of mass number, A in a nucleus

$r=r_0{A}^{1/3}.........\left(1\right)\mathrm{where}{r}_0=1.2\mathrm{fm}$

Calculation of the mass number

Using the given data in equation (1), we can get the mass number of the spherical nucleus as follows:

$$\begin{gathered} A={\left(\frac{r}{r_0}\right)}^3 \\ ={\left(\frac{3.6\mathrm{fm}}{1.2\mathrm{fm}}\right)}^3 \\ =27 \end{gathered}$$

Hence, the likely mass number is 27.