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In this work, we investigate the characteristics of the spin-singlet state$\eta_b$ of the bottomonia family via the radiative decays of $\Upsilon(nS)\to\eta_b+\gamma$. The theoretical estimation of the decay widths is carried outin terms of the light-front quark model (LFQM). Recently CLEO and BaBarcollaborations have measured $\mathcal{B}(\Upsilon(3S)\to\gamma\eta_b)$ and themass of ${\eta_b}$. In terms of the data we fix the concerned input parametersin our calculations of $\Upsilon(nS)\to \eta_b+\gamma$. A special attention ispaid on the transition of $\Upsilon(5S)\to \eta_b+\gamma$. The BELLE datashowed that the width of $\Upsilon(5S)\to \Upsilon(2S,1S)+\pi\pi$ is two orderslarger than that of $\Upsilon(4S)\to \Upsilon(2S,1S)+\pi\pi$, thus sometheoretical explanations have been proposed. Among them, it is suggested theinelastic final state interaction (IFSI) $\Upsilon(5S)\to B\bar B\to\Upsilon(1S)+\pi\pi$ may be a natural one. If so, a similar mechanism alsoapplies to $\Upsilon(5S)\to B^{(*)}\bar B^{(*)}\to \eta_b+\gamma$, the precisemeasurement would serve as a good test whether $\Upsilon(5S)$ possess exoticcomponents. Our calculation in the LFQM indicates that the rate of the directprocess $\Upsilon(5S)\to\eta_b+\gamma$ is not anomalous compared to$\Upsilon(mS)\to\eta_b+\gamma (m=1,2,3,4)$, thus if the IFSI does apply, therate of $\Upsilon(5S)\to\eta_b+\gamma$ should be larger than the others byorders.

Study on the radiative decays of $\Upsilon(nS)\to \eta_b+\gamma$