Calculating Chemical Shift: How do magnetic fields affect NMR frequencies?

[Lily Wright]

Homework Statement

In an NMR spectrum a CH₂ group has a peak centred at 9.81 ppm. What is the shift in Larmor frequency of the protons from that of an unshielded proton if the spectrometer magnetic field is 9.4 T? The magnetogyric ratio of an unshielded proton is γ_H = 26.75 × 10⁷ rad s^-1T^-1

2. The attempt at a solution
So 26.75 × 10⁷ rad s^-1T^-1 x 9.4 T = 2.51 x 10⁹ rad s^-1
x 0.159155 = 4.00 x 10⁹ Hz
/10⁶ = 400 MHz

Then I don't really know what to do
Chemical shift = v(sample)-v(reference)/v(reference)
9.81ppm = 10⁶ x (v(sample)- 4 x 10^-9/4 x 10^-9)
3924 = 10⁶ x (v(sample) x 10^-6 - 400)
4324 MHz for the sample frequency which I'm sure is wrong.

 

[Astronuc]

Can you write the relevant equations like the following? And perhaps cite the text.

http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/nmrcsh.html