Check the Clausius-Mossotti relation (Eq. 4.72) for the gases listed in Table 4.1. (Dielectric constants are given in Table 4.2.) (The densities here are so small that Eqs. 4.70 and 4.72 are indistinguishable. For experimental data that confirm the Clausius-Mossotti correction term see, for instance, the first edition of Purcell’s Electricity and Magnetism, Problem 9.28.)^{23}
\alpha=\frac{3 \epsilon_{0}}{N}\left(\frac{\epsilon_{r}-1}{\epsilon_{r}+2}\right) (4.72)
\chi_{e}=\frac{N \alpha}{\epsilon_{0}} (4.70)
| H | He | Li | Be | C | Ne | Na | Ar | K | Cs |
| 0.667 | 0.205 | 24.3 | 5.60 | 1.67 | 0.396 | 24.1 | 1.64 | 43.4 | 59.4 |
TABLE 4.1
| Material | Dielectric Constant | Material | Dielectric Constant |
| Vacuum | 1 | Benzene | 2.28 |
| Helium | 1.000065 | Diamond | 5.7-5.9 |
| Neon | 1.00013 | Salt | 5.9 |
| Hydrogen \left( H _{2}\right) | 1.000254 | Silicon | 11.7 |
| Argon | 1.000517 | Methanol | 33.0 |
| Air (dry) | 1.000536 | Water | 80.1 |
| Nitrogen \left( N _{2}\right) | 1.000548 | Ice (-30° C) | 104 |
| Water vapor (100° C) | 1.00589 | KTaNbO _{3}\left(0^{\circ} C \right) | 34,000 |
TABLE 4.2