An engineer is given a fixed volume $V_m$ of metal with which to construct a spherical pressure vessel. Assuming the vessel has thin walls and is pressurized to its bursting point,the amount of gas the vessel can contain,$n$ (in moles),depends only on $V_m$ $(m^3)$,the temperature $T$ $(K)$,the ideal gas constant $R$ $(J/(K \cdot mol))$,and the tensile strength of the metal $\sigma$ $(N/m^2)$. Which of the following gives $n$ in terms of these parameters?

• A
  $n = \frac{2}{3} \frac{V_m \sigma}{RT}$
• B
  $n = \frac{2}{3} \frac{\sqrt[3]{V_m \sigma}}{RT}$
• C
  $n = \frac{2}{3} \frac{\sqrt[3]{V_m \sigma^2}}{RT}$
• D
  $n = \frac{2}{3} \frac{\sqrt[3]{V_m^2 \sigma}}{RT}$