Final answer:
To find the initial kinetic energy of the hydrogen atom, conservation of energy and momentum must be applied to the system of the ${H}^{-}$ atom and ${Li}^{++}$ ion pre- and post-collision. Specific spectroscopic data or formulas from the Bohr model are needed to perform the calculation.
Step-by-step explanation:
The question involves a moving hydrogen atom (${H}^{-}$) colliding inelastically with a stationary lithium ion (${Li}^{++}$), with both particles initially in an excited state and ending up in different states post-collision without the emission of a photon. To calculate the kinetic energy of the ${H}^{-}$ atom before collision, we must consider the conservation of energy and linear momentum within the system.
Initially, the ${H}^{-}$ atom is in the first excited state, while the ${Li}^{++}$ ion is also in the first excited state but stationary. After the collision, the ${H}^{-}$ is observed to be in the ground state and the ${Li}^{++}$ in its second excited state.
Given the differences in energy levels of the ${H}^{-}$ atom and the ${Li}^{++}$ ion when they transition between states, we can use the conservation of energy to determine the initial kinetic energy of the hydrogen atom. However, since this is an inelastic collision, some of the initial kinetic energy must have been converted into potential energy or absorbed for the lithium ion to reach its higher state, following the conservation of total energy in the system.
Since the question does not provide the required energy levels or transition information for the ${H}^{-}$ atom and ${Li}^{++}$ ion, we would require these values to give a numerical answer. The information would typically be found in tables of spectroscopic data or can be calculated using formulas derived from the Bohr model of the atom.