Chapter 33, Problem 31P

To determine

Critical density in terms of the average number of nucleons per cubic meter.

Answer to Problem 31P

Critical density in terms of the average number of nucleons per cubic meter is $6{\text{ nucleons/m}}^3$

Explanation of Solution

Given:

The critical density for closure of the Universe is

  ${\rho }_{\text{c}}\approx {10}^{-26}{\text{ kg/m}}^3$

Calculation:

Mass of a typical nucleon is $1.67\times {10}^{-27}\text{ kg}$

Average number of nucleons per cubic meter is

  ${10}^{-26}{\text{kg/m}}^3\times \frac{1\text{ nucleon}}{1.67\times {10}^{-27}\text{ kg}}=6{\text{ nucleons/m}}^3$

Conclusion:

Thus, critical density in terms of the average number of nucleons per cubic meter is $6{\text{ nucleons/m}}^3$