 Solution

At room temperature, $k_{B}T$ is of order $0.026\mathrm{eV}$, far smaller than the electronic excitation gaps of the inferred hydrogenic ion. Ground-state absorption is therefore the natural interpretation. Assign the three lines to $1\to 2$, $1\to 3$, and $1\to 4$. Dividing each reciprocal wavelength by its corresponding factor $1-1/n^2$ givesThe small scatter is consistent with the rounded wavelength data. Since $R_{\infty }\simeq 1.0974\times 10^7{\mathrm{m}}^{-1}$ and $\mu \simeq m_e$,The ion is thus hydrogen-like lithium, ${\mathrm{Li}}^{2+}$. If “effective Rydberg constant” denotes only the reduced-mass constant rather than the charge-inclusive spectral coefficient, its value is $R_M\simeq R_{\mathrm{eff}}/9\simeq 1.097\times 10^7{\mathrm{m}}^{-1}$. The two conventions are explicitly distinguished; the rounded lines do not determine a precise isotope mass.