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The hyperfine splitting for the 2S charmonium state is calculated and thepredicted number is $\Delta_{\rm HF}(2S) = 57 \pm 8$ MeV, being by derivationthe lower bound of this splitting. It results in $M(\eta_c(2S))= 3630 \pm 8$MeV, which is smaller by two standard deviations than found in the Belleexperiment \cite{ref.01}, but close to the $\eta_c(2S)$ mass observed by thesame group in the experiment $e^+e^- \to J/\psi \eta_c$ \cite{ref.06} where$M(\eta_c(2S)) = 3622 \pm 12$ MeV was found.Comment: 8 pages RevTe

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mn /><mml:mo>(</mml:mo><mml:mn>3654</mml:mn><mml:mo>)</mml:mo><mml:mn /></mml:math>and hyperfine splitting in charmonium

ηc(3654)and hyperfine splitting in charmonium