The correct order of molar heat capacities measured at 298 K and 1 bar is :

To determine the correct order of molar heat capacities $$C_p$$ at $$298\text{ K}$$ and $$1\text{ bar}$$, we compare the physical states and molecular complexities of the given substances. Molar heat capacity represents the amount of heat required to raise the temperature of one mole of a substance by $$1\text{ K}$$.

Bromine, $$Br_2(l)$$, is a polyatomic liquid molecule possessing translational, rotational, and vibrational degrees of freedom. The presence of these additional modes of energy storage enables it to absorb a relatively large amount of heat before its temperature rises. Consequently, it has a high molar heat capacity.

Copper, $$Cu(s)$$, is a metallic solid whose heat capacity is mainly governed by lattice vibrations. Although solids have appreciable heat capacities, they generally possess fewer accessible degrees of freedom than complex liquid molecules, resulting in a lower molar heat capacity than liquid bromine.

Helium, $$He(g)$$, is a monatomic gas and possesses only translational degrees of freedom. According to the kinetic theory of gases, its molar heat capacity at constant pressure is

$$C_p=\frac{5}{2}R\approx20.8\text{ J K}^{-1}\text{ mol}^{-1},$$

making it the lowest among the given substances.

Hence, the correct order of molar heat capacities is

$$Br_2(l)>Cu(s)>He(g).$$

Therefore, the correct option is

$$Br_2(l)>Cu(s)>He(g).$$