In بِالدِّينِ, dāl follows the definite article and is a sun letter, so the article lām assimilates and the dāl is doubled.
In الَّذِي, the doubled lām results from lām meeting lām; do not change the dhāl or introduce an extra consonant.
At a pause on الدِّينِ, its final nūn becomes sākin after madd yāʾ, producing madd ʿāriḍ li-s-sukūn. In connection the final nūn has its ordinary vowel.
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Ad-dīn and alladhī: what happens to lām?
Al-Māʿūn and Al-Humazah: Applied Assimilation, Concealment, Madd and Hāʾ Rules
In بِالدِّينِ, dāl follows the definite article and is a sun letter, so the article lām assimilates and the dāl is doubled.
In الَّذِي, the doubled lām results from lām meeting lām; do not change the dhāl or introduce an extra consonant.
At a pause on الدِّينِ, its final nūn becomes sākin after madd yāʾ, producing madd ʿāriḍ li-s-sukūn. In connection the final nūn has its ordinary vowel.