Question

Calculate the relative number of nuclei of 13C (1 significant figure) in the higher and lower magnetic states at 19ºC in a magnetic field of 3.13 T.

Answer 1

The magnetic field strength is B₀ = 3.13T and T= 292 K

The ratio of number of nuclei in the higher(N_J) and lower magnetic states(N₀) is given by:

Nj = expl 2016T N = erpl-h7B

Now, k (Boltzman constant) =1.38 * 10^-23 JK^-1 , gyromagnetic ratio of 13C ($\gamma$) = 6.73 * 10⁷ rad.s^-1.T^-1  and h( Plank's constant) = 6.623 * 10^-34 Js

Putting the values we have,

expl- (6.73 x 10')(6.63 x 10-34)3.13 2 * 3.14 x 1.38 x 10-23 x 292 No

"] = f(-5.5188x10-6 NO

(correct to 1 significant figure)

N = 0.999 = 1.0 NO