Question

If the gyromagnetic ratio of proton is 42.58 MHz per Tesla, the resonance frequency for protons in a magnetic field of 1.5 Tesla is _______ MHz. (rounded off to two decimal places)

Hint:

The resonance frequency is directly proportional to the magnetic field strength and the gyromagnetic ratio. Use this relationship for calculating resonance frequencies in different magnetic fields.

Answer 1

The resonance frequency \( f \) for protons in a magnetic field \( B \) is given by the formula: \[ f = \gamma \cdot B \] Where:
\( f \) is the resonance frequency,
\( \gamma \) is the gyromagnetic ratio of the proton,
\( B \) is the magnetic field strength.
Given:
The gyromagnetic ratio of protons \( \gamma = 42.58 \, {MHz/T} \),
The magnetic field \( B = 1.5 \, {T} \).
Substitute the given values into the formula: \[ f = 42.58 \, {MHz/T} \times 1.5 \, {T} = 63.87 \, {MHz} \] Thus, the resonance frequency is: \[ \boxed{63.87 \, {MHz}} \]