\(\Delta E = 13.6{Z^2}\left( {\frac{1}{{n_1^2}} - \frac{1}{{n_2^2}}} \right)\,eV\)
\(47.2 = 13.6{Z^2}\left( {\frac{1}{{{2^2}}} - \frac{1}{{{3^2}}}} \right) = 13.6 \times \frac{5}{{36}}\,{Z^2}\)
\({Z^2} = \frac{{47.2 \times 36}}{{13.6 \times 5}} = 24.98\tilde - 25\)
\(⇒ Z = 5\)