what was their monetary system?
wuzhu coins is China's standard coin until the Tang dynasty and currencies.
Han dynasty
The Han dynasty inherited the "ban liang" coin type from the Qin. In the beginning of the Han, Emperor Gaozu closed the government mint in favor of private minting of coins. This decision was reversed in 186 BC by his widow Grand Empress Dowager Lü Zhi (d. 180 BC), who abolished private minting. In 182 BC, Lü Zhi issued a bronze coin that was much lighter in weight than previous coins. This caused widespread inflation that was not reduced until 175 BC when Emperor Wen allowed private minters to manufacture coins that were precisely 2.6 g (0.09 oz) in weight.

In 144 BC Emperor Jing abolished private minting in favor of central-government and commandery-level minting; he also introduced a new coin. Emperor Wu introduced another in 120 BC, but a year later he abandoned the "ban liangs" entirely in favor of the "wuzhu" (五銖) coin, weighing 3.2 g (0.11 oz). The "wuzhu" became China's standard coin until the Tang dynasty (618–907 AD). Its use was interrupted briefly by several new currencies
who was valued in han society under the philosophy of confucianism Emperor Gaozu of Han. can you mention few names of people of the royal family? Emperor Zhao (r. 87–74 BCE) , Emperor Yuan (r. 48–33 BCE)  Emperor Cheng (33–7 BCE) ,  Emperor He (r. 88–105 CE) ,  Emperor Shun (r. 125–144 CE) , Emperor Ling (r. 168–189 CE). was there slavery in this dynasty? Yes, Slaves comprised roughly 1% of the population. who was the founder of this dynasty? Liu Bang. what religion did people follow in this dynasty? They formed large hierarchical religious societies called the Way of the Five Pecks of Rice. did they have their own army? Yes, every male commoner aged twenty-three was liable for conscription into the military. have they contributed anything in science and technological field? The Han dynasty was a period of development of premodern Chinese science and technology, comparable to the level of scientific and technological growth what did they use for writing? Bronzewares, animal bones, and bamboo slips or wooden boards.
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Han dynasty [SEP] Currency
The Han dynasty inherited the "ban liang" coin type from the Qin. In the beginning of the Han, Emperor Gaozu closed the government mint in favor of private minting of coins. This decision was reversed in 186 BC by his widow Grand Empress Dowager Lü Zhi (d. 180 BC), who abolished private minting. In 182 BC, Lü Zhi issued a bronze coin that was much lighter in weight than previous coins. This caused widespread inflation that was not reduced until 175 BC when Emperor Wen allowed private minters to manufacture coins that were precisely 2.6 g (0.09 oz) in weight.