Q8 PE - College Physics (Urone)

Question

Find the radius of a \(^{{\rm{238}}}{\rm{Pu}}\) nucleus. \(^{{\rm{238}}}{\rm{Pu}}\)is a manufactured nuclide that is used as a power source on some space probes.

Step-by-Step Solution

Answer

The radius of the \(^{{\rm{238}}}{\rm{Pu}}\) particle is obtained as: \(7.437 \times {10^{ - 15}}\,{\rm{m}}\).

Step 1: 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.

Step 2: Evaluating the radius

The atomic mass number of the \(^{{\rm{238}}}{\rm{Pu}}\) particle is:

\(A = 238\)

The radius of \(^{{\rm{238}}}{\rm{Pu}}\) particle is:

\({R_o} = 1.2 \times {10^{ - 15}}\,{\rm{m}}\)

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

\(\begin{align}R &= \;{R_o}{A^{\frac{1}{3}}}\\ &= 1.2 \times {10^{ - 15}}\,m \times {(238)^{\frac{1}{3}}}\\ &= {\rm{ }}7.437 \times {10^{ - 15}}\,m\end{align}\)

Therefore, the radius is: \(7.437 \times {10^{ - 15}}\,{\rm{m}}\).