Please help answer both parts to the question. Hydrogen nuclei (protons) have sp
ID: 948447 • Letter: P
Question
Please help answer both parts to the question. Hydrogen nuclei (protons) have spin 1/2 just like an electron. We can distinguish two spin states"up" and "down". This direction describes the orientation of the magnetic moment of the nuclei. In an external magnetic field these two spin states have different potential energy. The difference in energy depends on the magnetic field applied: delta E = 2mu.B As you can see in the figures above, the greater the difference in energy, the more likely is the lower energy state populated. "Photons" (quanta of energy), can be used to provide the energy to let nuclei do a "spin-flip" and occupy temporarily the higher energy state. The energy of a single photon is: E = hf with h = 6.63 Times 10^-34 J.s, the Planck constant and f the frequency of the photon in units of Hz = s^-1. a) For "proton" MRI radio waves of 64 MHz are absorbed by hydrogen nuclei inside a patient that is tying in the MRI magnet and exposed to a strong field of 1.5 T. Calculate the energy (in eV) of one such radio wave photon.Explanation / Answer
Answer a):
The energy(E) of radiowave photon of 64MHz can be calculated by using following expression:
E = hf
Where, f = frequency in Hz
h = Plank’s constant = 6.626 x 10-34J.s
E = 6.626 x 10-34J.s x 64 x 106 Hz
E = 424.06 x 10-28J
E = 424.06 x 10-28J x( 6.242 x 1018 eV / 1 J)
E = 2647 x x 10-10 eV
Therefore, the energy of 64 MHz radio wave photon is 2647 x x 10-10 eV.
Ans b):
According to given expression E = 2B, it can be said that with decrease in value of magnetic field strength(B) the value of E decrease.
Thus, by reducing value of magnetic field from 1.5T to 1.0T, the value of E i.e. energy gap between the spin-up and spin-down states would decrease.
Since, expression for energy and frequency is E = hf, value of frequency(f) will decrease with decrease in value of energy (E). Therefore, for smaller energy gap the less frequency radio waves will be required.
Hence, no 64MHz radio wave photons would be absorbed.
Thus, following two options can be selected.
energy gap between the spin-up and spin-down states would decrease.
no 64MHz radio wave photons would be absorbed.