Question

Find the radius of a${}^{238}\mathrm{P}\mathrm{u}$nucleus.${}^{238}\mathrm{P}\mathrm{u}$is a manufactured nuclide that is used as a power source on some space probes.

Short answer

The radius of the ${}^{238}\mathrm{P}\mathrm{u}$ particle is obtained as: $7.437\times {10}^{-15}\mathrm{m}$.

Step-by-step solution

Define Radioactivity

The spontaneous emission of radiation in the form of particles or high-energy photons as a result of a nuclear process is known as radioactivity.

Evaluating the radius

The atomic mass number of the ${}^{238}\mathrm{P}\mathrm{u}$ particle is:

$A=238$

The radius of ${}^{238}\mathrm{P}\mathrm{u}$ particle is:

$R_o=1.2\times {10}^{-15}\mathrm{m}$

Using the following relation to obtain the value of radius as:

$\begin{array}{rl}R& =R_o{A}^{\frac{1}{3}}\\ & =1.2\times {10}^{-15}m\times (238{)}^{\frac{1}{3}}\\ & =7.437\times {10}^{-15}m\end{array}$

Therefore, the radius is: $7.437\times {10}^{-15}\mathrm{m}$.