Critical Potentials and the Heat of Dissociation of Hydrogen as Determined from its Ultra-Violet Band Spectrum

Abstract

Lyman has found that if a tube containing argon with a trace of hydrogen is excited by an uncondensed discharge, a simple spectrum is obtained that consists of twelve groups of lines of the secondary spectrum in the extreme ultraviolet. The group of shortest wave-length is partly obscured by one of the two extremely intense lines of argon, that correspond to its resonance potentials of 11.57 and 11.78 volts. The present investigation has shown that these groups are bands, due to the transitions from a single electronic and vibrational state, $A$, ${n}^{\ensuremath{'}}=a$ to the electronic and vibrational states $N$, ${n}^{\ensuremath{'}\ensuremath{'}}=0 \mathrm{to} 11$. These bands are apparently $Q$ branches with perturbations near the origin. The first lines fit the empirical formula $\ensuremath{\nu}=94075\ensuremath{-}4267 {n}^{\ensuremath{'}\ensuremath{'}}+113.5 {n}^{\ensuremath{'}\ensuremath{'}2}+\ensuremath{\cdots}$ The existance of a definite upper state is due to the argon, which, acting through limitation of electron velocities and collisions of the second kind, limits the energy that can be imparted to a hydrogen molecule to 11.78 volts. This is just sufficient to raise the molecule from the normal state $N$, $n=0$ to the excited state $A$, $n=a$. If $a=0$, the radiation potential for these bands is 11.61 volts, which agrees with the experimental values of the lowest radiation potential of the hydrogen molecule. The data permit the computation of the heat of dissociation, $D$, of the hydrogen molecule. The lower limit of $D$ is 4.10 volts or 94,600 calories per mol, and the upper limit 4.56 volts or 105,200 calories. The probable value is 4.34 volts or 100,100 calories. This is in agreement with the best experimental values.There is a remarkable parallelism between the atomic and molecular spectra of hydrogen, that seems to indicate that the electronic energy levels in the two cases must be very similar. An attempt was therefore made to introduce total electronic quantum numbers, ${e}_{t}$, and to compute the higher critical potentials of the hydrogen molecule. To the electronic level $N$ was assigned the value ${e}_{t}=1$ and to the level $A$ the value ${e}_{t}=2$. The ultra-violet band spectrum is due to the transitions ${e}_{t}\ensuremath{\geqq}2$ to ${e}_{t}=1$, and the visible spectrum to the transitions ${e}_{t}\ensuremath{\geqq}3$ to ${e}_{t}=2$. The higher critical potentials were computed by two methods, first, by use of the Glitscher diagram (in Sommerfeld's Atombau), and, secondly, by use of a Rydberg formula. The remarkable agreement between the values obtained by the two methods seems to indicate that these values have some significance. These values are 13.64, 14.32, 14.64, 14.81 volts, etc., giving an ionization potential of 15.19 volts. Several suggestions are made concerning the discrepancy between this value and the experimental values.