The Mobilities of Electrons in Hydrogen

Electron mobilities in pure hydrogen have been measured for pressures of 73 to 635 mm., using a modified alternating field method with fields up to 70 volts/cm. Undamped oscillation of 15,000 to 200,000 cycles were obtained from a vacuum tube oscillator and were measured with a precision wave-meter. By using a constant retarding potential of 6 volts the disturbing effect of ions of impurities was eliminated and curves without the usual feet were obtained. The mobility (reduced to a pressure of 76 cm.) is found to be best represented by the equation: $k=\frac{2.74\times {10}^6}{[399+(\frac{\mathrm{Vo}}{d}\left)\right(\frac{760}{p^{\frac{3}{4}}}]}$, where $\frac{\mathrm{Vo}}{d}$ is the critical field in volts per cm. and $p$ is the pressure in mm. Comparison with kinetic theory. This equation is practically of the same form as that found by less accurate measurements for nitrogen and since it differs from Townsend's theoretical equation: $k=\frac{a}{{[b+(\frac{\mathrm{Vo}}{d}\left)\right(\frac{760}{p}\left)\right]}^{\frac{1}{2}}}$, either the mean free path of the electron or its loss of energy at impact are probably functions of the velocity of the electron. When the electrical fields are small the mobility at atmospheric pressure comes out 68.6 $\frac{m}{sec}$. whereas the kinetic theory gives 130.6; hence the actual mean free path must be only about half that assumed by the theory.