Question

In an MRI, one detects the absorption and emission of radiation as spins flip back and forth in a magnetic field. The energy of the radiation emitted or absorbed when a spin flips is given by: gghB (2) 2m. where g is typically 2, q is the charge of the spinning object, m is its mass, and B is the magnetic field strength. (a) (2 points) A clinical MRI detects a signal from protons flipping up and down. If the frequency of the radiation is f J 23MHz, what is the magnetic field in the machine? (b) (2 points) If we put an electron g 2 in that same magnetic field, what would be the frequency of the radiation emitted when the spin flips?

Answer 1

E=hv

h is plank's constant and v is frequency

E=6.626 x 10^-34*23*10^6

E=152.398*10^-28 J

a)E=gqhB/2m

2Em/ghq=B

2*152.398*10^-28*1.67*10^-27/2*6.626 x 10^-34*1.6*10^-19

B=508.95*10^-55/21.2*10-53

B=24*10^-2 T

b) if g=2 then

E=gqhB/2m

E=2*1.6*10^-19*6.626 x 10^-34*24*10^-2/2*(9.1*10^-31)

E=508.9*10^-55/18.2*10^-31

E=27.97*10^-24 J

E=hv

27.97*10^-24/6.626 x 10^-34=v

4.23*10^10 Hz=v