Final answer:
The magnetic field strength for resonance for a proton frequency of 670 MHz in an NMR spectrometer is calculated using the Larmor equation and is found to be 15.7 T.
Step-by-step explanation:
To calculate the magnetic field strength ("B") for resonance when the frequency ("f") of a proton in an NMR spectrometer is 670 MHz, you can use the Larmor equation which relates the magnetic field and frequency for a particle with a gyromagnetic ratio ("γ"). The Larmor equation is given by:
f = γ * B / (2π)
The gyromagnetic ratio for the proton is approximately 42.576 MHz/T. We can rearrange the Larmor equation to solve for B:
B = 2π * f / γ
Substituting the given frequency:
B = 2 * π * 670 MHz / 42.576 MHz/T
B = 15.7 T
Therefore, the magnetic field strength for resonance at a frequency of 670 MHz for a proton in an NMR spectrometer is 15.7 T, which corresponds to option c.