\(\cfrac{a_{\psi\,\pi}}{a_{\psi\,ne}}\lt 1.5\)
at the limit,
\(\cfrac{a_{\psi\,\pi}}{a_{\psi\,ne}}=1.5\)
obviously,
\(a_{\psi\,ne}=\cfrac{2}{3}a_{\psi\,\pi}\)
and
\(2a_{\psi\,ne}=\cfrac{4}{3}a_{\psi\,\pi}\gt a_{\psi\,\pi}\)
Since, \(2a_{\psi\,ne}\gt a_{\psi\,\pi}\) particles of this size do no occur normally. These particles occur only under higher energy conditions; high acceleration, high temperature and/or high voltage.
So, \(n_2=2n_e\) to \(n_1=n_e\) energy transition is the first to be seen as high energy conditions are applied, although it is not necessarily the lowest absorption line (least \(\lambda\), highest energy). When \(3n_e\) size particles are possible given higher energy conditions, transitions from \(n_3=3n_e\) to \(n_2=2n_e\), \(n_3=3n_e\) to \(n_1=n_e\) are possible. It is likely that these lines sandwich the first line between them.
These transitions do not reverse because the resultant particles are positively charge or neutral.
Since, \(n_e\) particles are neutral, high collision rate under high energy conditions will force them to fuse and the reverse transition \(n_1=n_e\) to \(n_2=2n_e\) emits a spectral line. In this way, the first line fades when higher energy conditions are applied. The appearance of other absorption lines on the spectrum, sees the fading of the first line and other lines involving \(n_1=n_e\), ie the first series.
Good morning.
