我們利用PS質量方程、星系團質量-溫度及星系團X射線亮度-溫度關係導出星系團的X射線亮度方程。利用此方程可估計星系團間介質對X射線背景輻射的貢獻，並藉由代換不同的星系團質量-溫度關係以對星系團之動力學性質做一討論。本論文中我們展現了在不同的宇宙論模型下，星系團在1~10 keV範圍的光譜。與未解析出的X射線背景輻做一比較後，我們對星系團的數量分佈及動力學模型的限制做一討論。 We present estimates of the X-ray background (XRB) emission from the intra-cluster medium associated with groups and clusters of galaxies. We use the X-ray luminosity function (XLF) that derived from the Press-Schechter mass function, the mass-temperature (M-T), and the X-ray luminosity-temperature relations. We have applied different M-T relations in the XLF to estimate the XRB. Our results can provide constraints on the dynamical properties of groups and clusters of galaxies. Here we show the 1~10 keV X-ray spectra from groups and clusters of galaxies under different cosmological models and compared the summing up X-ray emission from groups and clusters of galaxies with the unresolved diffuse XRB. We discuss the constraints on the distribution and the dynamical evolution model of the groups and clusters of galaxies.