What is the approximate Larmor precessional frequency of a hydrogen proton in a static magnetic field of 0.5T?

• A. 14.0 mHz
• B. 21.233 mHz
• C. 28.0 mHz
• D. 35.5 mHz

Answer: (B)

The Larmor precessional frequency is calculated using the formula:

[ f = \frac{\gamma}{2\pi} \times B_0 ]

where ( \gamma ) (the gyromagnetic ratio for a hydrogen proton) is approximately ( 42.58 , \text{MHz/T} ), and ( B_0 ) is the strength of the magnetic field in Tesla.

Given a magnetic field strength of 0.5T, substituting the values into the formula provides the following calculation:

1. First, compute ( \gamma \times B_0 ):

[ 42.58 , \text{MHz/T} \times 0.5 , \text{T} = 21.29 , \text{MHz} ]

2. Convert this frequency into hertz (Hz):

[ 21.29 , \text{MHz} = 21.29 \times 10^6 , \text{Hz} ]

3. Divide by ( 2\pi ) to find the Larmor frequency:

[ f = \frac{21.29 \times 10^6}{2\pi} \