Does dry ablution (tayammum) invalidate the prayer due to a broken right hand?

If a limb used for ablution (wudu) or ritual bath (ghusl) is broken, the wound is either exposed or covered.

If the wound is exposed: The sound part must be washed. If washing is not possible, it should be wiped. If wiping is not possible, then tayammum (dry ablution) should be performed for the injured limb, in accordance with the verse: "So fear Allah as much as you are able."

If the wound is covered with a splint (jabeerah): The sound part must be washed, and the splint should be wiped over. In this case, tayammum and wiping over the injured limb are not combined, unless the splint exceeds the necessary size. In that instance, tayammum should be performed for the area of the wound, and the part of the sound body covered by the splint should be wiped over, while the rest of the body is washed.