You asked:

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

No
Elisabeth Ludovika of Bavaria
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

Frederick William IV of Prussia (1795-1861), the King of Prussia (1840-1861)

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