Physics of Spine Excitation of Hydrogen and Electromagnetic Field
This course explores the principles behind the spin excitation of hydrogen nuclei in the presence of electromagnetic fields. This concept is fundamental in technologies like Magnetic Resonance Imaging (MRI).
Module 1: Hydrogen Nucleus Spin
Hydrogen nuclei (protons) behave as tiny magnets due to their intrinsic spin. In a magnetic field, the spin of the hydrogen nuclei can align in specific directions, either parallel or anti-parallel to the field.
Formula:
Magnetic Moment (μ):
μ = γ * I
where
μ = magnetic moment of the hydrogen nucleus (Am²)
γ = gyromagnetic ratio (42.58 MHz/T for hydrogen)
I = spin angular momentum (in units of ħ, the reduced Planck constant)
Example Calculation:
Calculate the magnetic moment for a hydrogen nucleus with a spin angular momentum of 1/2 ħ in a magnetic field.
Given: γ = 42.58 MHz/T and I = 1/2, we can calculate:
μ = (42.58 × 106 Hz/T) * (1/2) × ħ
μ = 21.29 × 106 Hz/T * 1.05457 × 10-34 J·s ≈ 2.24 × 10-28 Am²
Module 2: Excitation of Hydrogen Spins
When a hydrogen nucleus is exposed to an alternating magnetic field of the same frequency as its precessional frequency, it absorbs energy and "flips" its spin from a low-energy state (aligned with the magnetic field) to a high-energy state (anti-parallel to the field).
Formula:
Precessional Frequency (f0):
f0 = γ * B
where
f0 = precessional frequency of the hydrogen nucleus (Hz)
γ = gyromagnetic ratio (42.58 MHz/T for hydrogen)
B = magnetic field strength (T)
Example Calculation:
Calculate the precessional frequency of a hydrogen nucleus in a magnetic field of 1.5 T.
Given: γ = 42.58 MHz/T and B = 1.5 T, we can calculate:
f0 = (42.58 × 106 Hz/T) * (1.5 T) ≈ 63.87 MHz
Module 3: Electromagnetic Field Interaction
The hydrogen spins interact with the electromagnetic field through resonance. When the field frequency matches the precessional frequency of the spins, the hydrogen nuclei absorb energy, which is then released as electromagnetic radiation when the spin flips back to its lower energy state.
Formula:
Energy Absorbed (E):
E = h * f0
where
E = energy absorbed (J)
h = Planck's constant (6.626 × 10-34 J·s)
f0 = precessional frequency (Hz)
Example Calculation:
For the hydrogen nucleus in a 1.5 T field with a precessional frequency of 63.87 MHz, calculate the energy absorbed.
Given: f0 = 63.87 × 106 Hz, we can calculate:
E = (6.626 × 10-34 J·s) * (63.87 × 106 Hz) ≈ 4.23 × 10-27 J
Module 4: Applications in MRI
In MRI, the principles of hydrogen spin excitation are used to create detailed images of the body. By manipulating the magnetic field and using radiofrequency pulses, MRI scanners induce spin flips in hydrogen nuclei, which then emit signals that are detected and used to generate images of tissues.
Note: MRI is particularly sensitive to hydrogen, as the human body is mostly composed of water (H₂O), which contains hydrogen nuclei.