You asked:

was frederick william iv of prussia younger than elisabeth ludovika of bavaria

No. Frederick William IV of Prussia is not younger than Elisabeth Ludovika of Bavaria.

Elisabeth Ludovika of Bavaria (November 13, 1801 - December 14, 1873), the Princess of Bavaria and later Queen consort of Prussia

Frederick William IV of Prussia
Frederick William IV of Prussia
Frederick William IV of Prussia

King Frederick William IV of Prussia (October 15, 1795 - January 2, 1861), the eldest son and successor of Frederick William III of Prussia, reigned as King of Prussia from 1840 to 1861

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