A sample of paramagnetic material containing \(10^{25}\) atoms is placed in an external field magnetic field of 1 tesla at room temperature. Assume that the electrons of each atom have zero orbital angular momentum and spin angular momentum of 1/2. Thus, J=1/2 and g=2.
a) Find the total magnetic moment of the sample.
b) What would be the total magnetic moment at a temperature of 0.1K?