Why did china prosper under the Han dynasty

Because there was peace and cultural development.

Explanation:

The strong but benevolent Han dynasty began a golden age of reform and expansion. The first period, called Western Han, lasted until 9 AD.

The Han Dynasty ended the civil war and reunited China in 202 BC, ushering in a golden age of peace and prosperity, during which progress and cultural development took place. The Western Han period continued with many of Qin's policies, but modified them with Confucian ideals. Because of this, the Han lasted much longer than the harsh Qin Dynasty - The Western Han period in particular lasted until 9 CE, when there was a brief rebellion. One of the most exalted Han emperors was Emperor Wu. He made Confucianism the official philosophy, encouraged reciprocity between the state and its people, reformed the economy and agriculture, made contact with India, defended China from the Huns, and doubled the size of the empire. Rebellions and external threats posed challenges to the Western Han, but managed to survive.

In 202 B. C. the Han dynasty established one of the most successful and peaceful periods in the Chinese history. It allowed the Chinese people to prosper in peace since life was more harmonious than during the Warring States period (403-221 B. C. E.)