Two-Body<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">B</mml:mi></mml:math>Meson Decays to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>η</mml:mi></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>: Observation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">B</mml:mi><mml:mi/><mml:mo>→</mml:mo><mml:mi/><mml:mi>η</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="italic">K</mml:mi></mml:mrow><mml:mrow><mml:mi>*</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>

In a sample of $19\ifmmode\times\else\texttimes\fi{}{10}^{6}$ produced $B$ mesons, we have observed the decays $B\ensuremath{\rightarrow}\ensuremath{\eta}{K}^{*}$ and improved our previous measurements of $B\ensuremath{\rightarrow}{\ensuremath{\eta}}^{\ensuremath{'}}K$. The branching fractions we measure for these decay modes are $B({B}^{+}\ensuremath{\rightarrow}\ensuremath{\eta}{K}^{*+})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({26.4}_{\ensuremath{-}8.2}^{+9.6}\ifmmode\pm\else\textpm\fi{}3.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, $B({B}^{0}\ensuremath{\rightarrow}\ensuremath{\eta}{K}^{*0})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({13.8}_{\ensuremath{-}4.6}^{+5.5}\ifmmode\pm\else\textpm\fi{}1.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, $B({B}^{+}\ensuremath{\rightarrow}{\ensuremath{\eta}}^{\ensuremath{'}}{K}^{+})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({80}_{\ensuremath{-}9}^{+10}\ifmmode\pm\else\textpm\fi{}7)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, and $B({B}^{0}\ensuremath{\rightarrow}{\ensuremath{\eta}}^{\ensuremath{'}}{K}^{0})\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}({89}_{\ensuremath{-}16}^{+18}\ifmmode\pm\else\textpm\fi{}9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$. We have searched with comparable sensitivity for related decays and report upper limits for these branching fractions.