Dowry usually is decided at the time of Nihah that the woman will be entitle to get whatever valuable is decided then. So she can claim for half of the appointed dowry. If not dowry was fixed the man should give her something as a gesture of goodwill and manhood. See the following verses:
لَا جُنَاحَ عَلَیۡکُمۡ اِنۡ طَلَّقۡتُمُ النِّسَآءَ مَا لَمۡ تَمَسُّوۡہُنَّ اَوۡ تَفۡرِضُوۡا لَہُنَّ فَرِیۡضَۃً ۚۖ وَّ مَتِّعُوۡہُنَّ ۚ عَلَی الۡمُوۡسِعِ قَدَرُہٗ وَ عَلَی الۡمُقۡتِرِ قَدَرُہٗ ۚ مَتَاعًۢا بِالۡمَعۡرُوۡفِ ۚ حَقًّا عَلَی الۡمُحۡسِنِیۡنَ
وَإِن طَلَّقْتُمُوهُنَّ مِن قَبْلِ أَن تَمَسُّوهُنَّ وَقَدْ فَرَضْتُمْ لَهُنَّ فَرِيضَةً فَنِصْفُ مَا فَرَضْتُمْ إِلَّا أَن يَعْفُونَ أَوْ يَعْفُوَ الَّذِي بِيَدِهِ عُقْدَةُ النِّكَاحِ ۚ وَأَن تَعْفُوا أَقْرَبُ لِلتَّقْوَىٰ ۚ وَلَا تَنسَوُا الْفَضْلَ بَيْنَكُمْ ۚ إِنَّ اللَّهَ بِمَا تَعْمَلُونَ بَصِيرٌ
And there is no blame on you in the matter of dower if you divorce women before touching them or before having fixed their dower; but this should definitely be the case that you bestow on them some resources of life according to the norms when you send them off, the high in status according to their means, and the poor according to theirs. This is an obligation on those who are thorough.
But if you divorce them before touching them, yet after the fixing of a dower for them, then half of this fixed dower should be given to them, unless they forgo it or he forgoes it in whose hands is the marriage knot; [622] and it is nearer to piety that you men forgo your right. And do not forget your superiority among yourselves. Indeed, God is observing what you are doing. (2: 236-237)