A solid at temperature is placed in an external magnetic field B 1 Tesla = 1x 104 gauss. The solid contains weakly interacting paramagnetic atoms of spin 1/2, so that the energy of each atom is ±µB. h x a. If the magnetic moment is equal to one Bohr magneton, i.e., µ 1.4 MHz/gauss, below what temperature must one cool the solid so that more than 75% of the atoms are polarized with their spins parallel to the external magnetic field? = b. Suppose that one considered instead a solid which is free of paramagnetic atoms but contains many protons (e.g., paraffin). Each proton has spin 1/2 and a magnetic moment p h x 2.1 kHz/gauss. At the same temperature as you determined in part a., what fraction of protons will have their spins aligned parallel to the external magnetic field? -

A solid at temperature is placed in an external magnetic field B 1 Tesla = 1x 104 gauss. The solid contains weakly interacting paramagnetic atoms of spin 1/2, so that the energy of each atom is ±µB. h x a. If the magnetic moment is equal to one Bohr magneton, i.e., µ 1.4 MHz/gauss, below what temperature must one cool the solid so that more than 75% of the atoms are polarized with their spins parallel to the external magnetic field? = b. Suppose that one considered instead a solid which is free of paramagnetic atoms but contains many protons (e.g., paraffin). Each proton has spin 1/2 and a magnetic moment p h x 2.1 kHz/gauss. At the same temperature as you determined in part a., what fraction of protons will have their spins aligned parallel to the external magnetic field? -