In an MRI, one detects the absorption and emission of radiation as spins flip ba

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?

Explanation / Answer

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

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