[poonilization]

Hi, i'm having a little trouble with this example we went through during lectures. http://i.gyazo.com/147dd0540e365077c7894eab7d1dc02e.png

I understand there are more nuclei alligned parallel to the external magnetic field (B₀) and therefore N_1/2 > N_-1/2

You sub ΔE, k and T into the equation and get 1.0000479 as the ratio of N_1/2 to N_-1/2, and that in 1 mole N_1/2 + N_-1/2 has to = N_A

but i dont understand how to calculate the exact number of nucleii in the spin up state (N_1/2) and spin down state (N_-1/2)

Could anyone please explain how i would get to the exact number of spin up states (N_1/2) and spin down states (N_-1/2) given in the example?

[mjc123]

You have N_1/2/N_-1/2 = 1+δ, where δ is very small. In this case we can make the accurate approximation
N_1/2 = 1/2 N_A(1+δ/2) and N_-1/2 = 1/2 N_A(1-δ/2)
because N_1/2/N_-1/2 = (1+δ/2)(1-δ/2)^-1 = (1+δ/2)(1+δ/2+...) and powers of δ higher than 1 can be ignored.

[poonilization]

Thank you very much, makes more sense now