Praise be to Allah.
There is no specific amount which must be recited in Taraaweeh prayer, but the longer it is the better, so long as that does not cause hardship for the members of the congregation.
Al-Albaani (may Allaah have mercy on him) said:
With regard to recitation in night prayers (qiyaam) in Ramadaan and at other times, the Prophet (peace and blessings of Allaah be upon him) did not set a specific limit and state that one is not allowed to do more or less than that. Rather his recitation in Taraaweeh used to vary, sometimes being short and sometimes being long. Sometimes he would recite in each rak’ah a verse which was equivalent in length to al-Muzammil, which is twenty verses long, and sometimes he would recite something that was fifty verses long. And he (peace and blessings of Allaah be upon him) used to say: “Whoever prays with a hundred verses at night will not be recorded as one of the negligent.”
According to another hadeeth, “… with one hundred verses, he will be recorded as one of the devout and sincere.”
The Prophet (peace and blessings of Allaah be upon him) recited the seven long ones in prayer at night when he was sick. These are: al-Baqarah, Aal ‘Imraan, al-Nisa’, al-Maa'idah, al-An’aam, al-A’raaf and al-Tawbah.
In the story of the prayer of Hudhayfah ibn al-Yamaan praying behind the Prophet (peace and blessings of Allaah be upon him), it states that in one rak’ah he (peace and blessings of Allaah be upon him) recited al-Baqarah, then al-Nisa’, then Aal ‘Imraan, and he recited them at a slow and deliberate pace.
It is narrated with the soundest of isnaads that when ‘Umar (may Allaah be pleased with him) commanded Ubayy ibn Ka’b to lead the people in praying eleven rak’ahs during Ramadaan, Ubayy (may Allaah be pleased with him) used to recite the hundreds (i.e., the soorahs with more than 100 verses), until those who were behind him used to lean on sticks because of the length of the recitation, and they did not depart until shortly before Fajr.
It is narrated in another saheeh report that ‘Umar would call the reciters in Ramadaan, and he would tell those who were quickest in recitation to recite thirty verses, those who were moderate in the speed of recitation to recite twenty-five, and those who recited slowly to recite twenty.
Based on this, if a person is praying qiyaam by himself, he may make it as long as he wants. The same applies if the ones who are praying with him are similar to him in stamina. The longer it is the better, but he should not make it so long that he spends the whole night awake, expect occasionally, following the Prophet (peace and blessings of Allaah be upon him) who said: “The best of guidance is the guidance of Muhammad.”
But if he is leading others in prayer, then he should make it only so long as not to cause hardship to those who are praying behind him, because the Prophet (peace and blessings of Allaah be upon him) said: “When any one of you leads the people in prayer, let him make the prayer short, because among them are the young, the elderly, the weak, the sick and those who are in need. But if he is praying qiyaam by himself, let him make his prayer as long as he wants.
End quote from Risaalat Qiyaan Ramadaan
See also the question no : (66504).