Q6 PE - College Physics (Urone)

Question

Find the length of a side of a cube having a mass of \(1.0\,{\rm{kg}}\) and the density of nuclear matter, taking this to be \(2.3 \times {10^{17}}\,{\rm{kg/}}{{\rm{m}}^{\rm{3}}}\).

Step-by-Step Solution

Answer

The length of the side of the cube is obtained as: \(1.632x{10^{ - 6}}\,{\rm{m}}\).

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 length of the side of a cube

The mass of the nuclear matter is:

\(m = 1\,{\rm{kg}}\)

The density of the nuclear matter is:

 

The relation used to evaluate the density of the nuclear matter is:

\(\begin{align}p &= \frac{m}{V}\\ &= \frac{M}{{{L^3}}}\end{align}\)

Rearranging and solving to obtain the length of the side of cube as:

\(\begin{align}L &= {\left( {\frac{m}{p}} \right)^{\frac{1}{3}}}\\ &= {\left( {\frac{{1\,kg}}{{2.3x{{10}^{17}}\,kg/m}}} \right)^{\frac{1}{3}}}\\ &= 1.632x{10^{ - 6}}\,m\end{align}\)

 

Therefore, the length of side of cube is: \(1.632x{10^{ - 6}}\,{\rm{m}}\).