To calculate the magnetic susceptibility of a molecule, we need to determine the magnetic moment of the molecule and then use the Curie law. The magnetic moment can be calculated using the formula: = gJ * B * J J+1 where gJ is the Landé g-factor, B is the Bohr magneton 9.274 x 10^-24 J/T , and J is the total angular momentum quantum number.The Landé g-factor gJ can be calculated using the formula:gJ = 3J J+1 + S S+1 - L L+1 / 2J J+1 Plugging in the given quantum numbers S=1, L=2, and J=3/2 :gJ = 3 3/2 5/2 + 1 2 - 2 3 / 2 3/2 5/2 gJ = 15/2 + 2 - 6 / 15gJ = 1/2Now, we can calculate the magnetic moment : = 1/2 * 9.274 x 10^-24 J/T * 3/2 5/2 = 0.5 * 9.274 x 10^-24 J/T * 15/4 = 4.637 x 10^-24 J/TNow, we can use the Curie law to calculate the magnetic susceptibility : = n * ^2 / 3 * k * T where n is the number of molecules per unit volume, k is the Boltzmann constant 1.381 x 10^-23 J/K , and T is the temperature in Kelvin. However, we are asked to find the magnetic susceptibility in cm^3 mol^-1, so we need to modify the formula to: = N_A * ^2 / 3 * k * T where N_A is Avogadro's number 6.022 x 10^23 mol^-1 .Assuming room temperature T = 298 K : = 6.022 x 10^23 mol^-1 * 4.637 x 10^-24 J/T ^2 / 3 * 1.381 x 10^-23 J/K * 298 K = 6.022 x 10^23 mol^-1 * 2.149 x 10^-47 J^2/T^2 / 1.237 x 10^-20 J K^-1 = 1.293 x 10^-27 cm^3 mol^-1So, the magnetic susceptibility of the molecule in the presence of an external magnetic field of 0.5 T is approximately 1.293 x 10^-27 cm^3 mol^-1.