Magnetic resonance imaging (MRI) scans are being used for medical diagnostics with a lot of success. The proton of any atom behaves like a current carrying loop or a magnetic dipole. When an external magnetic field is applied, this dipole tends to align itself in the direction of the magnetic field. There can be two possible orientations of this dipole. [1] Parallel to the magnetic field. [2] Antiparallel to the magnetic field. Since the potential energy of a current carrying loop in magnetic field is given by U = - \overset{\rightarrow}{M} \cdot \overset{\rightarrow}{B}, there is a difference of energy in these two possible orientations. ΔE = 2MB Any given sample tends to be in position of minimum potential energy (orientation-1). It can absorb a photon of appropriate energy to jump to orientation-2. This leads to reversal of spin of the proton. In any sample, normally only protons of hydrogen atom can easily respond to this reversal of spin. But the magnetic field used here is actually the net magnetic field at the location of proton. It is a vector sum of external magnetic field and the internal magnetic field set up by the atoms. Different hydrogen atoms have dfferent internal magnetic fields. eg. in ethanol. The hydrogen atom of OH group, hydrogen atom of CH2 group and hydrogen atom of CH3 group each have different internal magnetic field. If we keep the frequency of incident photons as constant while increasing the external magnetic field. The energy absorbed by ethanol at different Bext is plotted. This spectrum is unique to every group. This graph forms a signature by which we can identify the groups of organic atoms.

Magnetic resonance imaging (MRI) scans are being used for medical diagnostics with a lot of success. The proton of any atom behaves like a current carrying loop or a magnetic dipole. When an external magnetic field is applied, this dipole tends to align itself in the direction of the magnetic field. There can be two possible orientations of this dipole.

[1] Parallel to the magnetic field.

[2] Antiparallel to the magnetic field.

Since the potential energy of a current carrying loop in magnetic field is given by

U = $- \vec{M} \cdot \vec{B}$ , there is a difference of energy in these two possible orientations.

ΔE = 2MB

Any given sample tends to be in position of minimum potential energy (orientation-1). It can absorb a photon of appropriate energy to jump to orientation-2. This leads to reversal of spin of the proton.

In any sample, normally only protons of hydrogen atom can easily respond to this reversal of spin. But the magnetic field used here is actually the net magnetic field at the location of proton. It is a vector sum of external magnetic field and the internal magnetic field set up by the atoms. Different hydrogen atoms have dfferent internal magnetic fields. eg. in ethanol.

The hydrogen atom of OH group, hydrogen atom of CH₂ group and hydrogen atom of CH₃ group each have different internal magnetic field. If we keep the frequency of incident photons as constant while increasing the external magnetic field. The energy absorbed by ethanol at different B_ext is plotted.

This spectrum is unique to every group. This graph forms a signature by which we can identify the groups of organic atoms.

Linked Question 1

The magnetic dipole moment of proton in H-atom of water molecule is 1.5 × 10^–26 J/T. Internal magnetic field is negligible. What is the wavelength of photon required for reversal of spin of proton, if external magnetic field is 2.21 T.

3 m

6 m

1 m

2 m

$\frac{hc}{λ} = 2 MB$

$λ = \frac{hc}{2 MB} = \frac{6.63 \times 10^{- 34} \times 3 \times 10^{8}}{2 \times 1.5 \times 10^{- 26} \times 2.21} = 3 m$

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Linked Question 2

A hydrogen atom can be in 3 different positions in a variable magnetic field whose lines are shown below. In which of the case will the maximum photon energy be required to reverse the spin ? (In all 3 positions $\vec{M}$ is parallel to $\vec{B}$ )

all 3 require same energy

ΔE = 2MB

B₁ > B₂ > B₃

⇒ ΔE₁ > ΔE₂ > ΔE₃

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Linked Question 3

If the net magnetic field due to all the atoms is in the same direction as the external magnetic field, choose the correct statement.

Internal magnetic field at H of CH2 group is maximum.

Internal magnetic field at H of CH3 group is maximum.

Internal magnetic field at H of OH group is maximum.

Internal magnetic field at H of all three groups are equal.

ΔE = 2MB = same

$B = \frac{ΔE}{2 M}$ = B_ext + B_in

B_ext is maximum ⇒ B in is minimum.

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