An engineer is given a fixed volume V_{m} of metal with which to construct a spherical pressure vessel. Interestingly, assuming the vessel has thin walls and is always pressurized to near its bursting point, the amount of gas the vessel can contain, n (measured in moles), does not depend on the radius r of the vessel; instead it depends only on V_{m} (measured in \mathrm{m}^{3} ), the temperature T (measured in \mathrm{K} ), the ideal gas constant R (measured in \mathrm{J} /(\mathrm{K} \cdot \mathrm{mol}) ), and the tensile strength of the metal \sigma (measured in \mathrm{N} / \mathrm{m}^{2} ). Which of the following gives n in terms of these parameters?
Answer Choices
A. n=\frac{2}{3} \frac{V_{m} \sigma}{R T}
B. n=\frac{2}{3} \frac{\sqrt[3]{V_{m} \sigma}}{R T}
C. n=\frac{2}{3} \frac{\sqrt[3]{V_{m} \sigma^{2}}}{R T}
D. n=\frac{2}{3} \frac{\sqrt[3]{V_{m}^{2} \sigma}}{R T}
E. n=\frac{2}{3} \sqrt[3]{\frac{V_{m} \sigma^{2}}{R T}}