Step 1: Understanding the Concept:
A "hydrogen-like species" is an atom or ion that contains only one single electron.
The Bohr model of the atom was initially developed for hydrogen and can only be strictly applied to such single-electron systems.
To identify if a species is hydrogen-like, we must calculate its total number of electrons.
Step 2: Key Formula or Approach:
A hydrogen-like species contains exactly one electron.
Calculate the number of electrons for each ion using the formula: \(\text{Number of electrons} = \text{Atomic Number } (Z) - \text{Charge}\).
Step 3: Detailed Explanation:
Let's determine the number of electrons for each given option:
(A) \(\text{Li}^{+2}\): Lithium has an atomic number \(Z = 3\). The ion has a charge of \(+2\), meaning it has lost 2 electrons.
Number of electrons = \(3 - 2 = 1\). This is a single-electron system, so it is hydrogen-like.
(B) \(\text{Be}^{+3}\): Beryllium has an atomic number \(Z = 4\). The ion has a charge of \(+3\), meaning it has lost 3 electrons.
Number of electrons = \(4 - 3 = 1\). This is a single-electron system, so it is hydrogen-like.
(D) \(\text{He}^{+}\): Helium has an atomic number \(Z = 2\). The ion has a charge of \(+1\), meaning it has lost 1 electron.
Number of electrons = \(2 - 1 = 1\). This is a single-electron system, so it is hydrogen-like.
(C) \(\text{Li}^{+}\): Lithium has an atomic number \(Z = 3\). The ion has a charge of \(+1\), meaning it has lost 1 electron.
Number of electrons = \(3 - 1 = 2\).
Because \(\text{Li}^+\) contains two electrons, it is a multi-electron system (specifically, it is "helium-like").
Therefore, it does not fit the definition of a hydrogen-like species.
Step 4: Final Answer:
\(\text{Li}^{+}\) is not a hydrogen-like species.