NMR has two magnetic fields, one from the static external magnetic field, B0B0, generally to be in the zz-direction and

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NMR has two magnetic fields, one from the static external magnetic field, B0B0, generally to be in the zz-direction and the other from from the incoming oscillating magnetic field, B1B1, from a radiation in the radio-frequency range of electromagnetic spectrum, represented as B1=B01cos2πνtB1=B10cos⁡2πνt. This oscillating field interacts with nuclear spin moments αα and ββ from proton resulting in transitions between the energy states which is seen as NMR spectrum.
During the lecture hours we learnt that the probability of transition is defined by the dipole moment integral ⟨ψ∗iHˆψj⟩⟨ψi∗H^ψj⟩ where the HH is the Hamiltonian operator that causes the transition.
In the case of NMR, the oscillating B1B1 field induces the transition and so the probability of transition between the two spins and thus the selection rule can be found. Identifying Hˆ=−μˆ⋅B→1=−γIˆ⋅B→1H^=−μ^⋅B→1=−γI^⋅B→1 predict the NMR transition selection rule from Pk=∫ψ∗iHˆψjdτPk=∫ψi∗H^ψjdτ where k=x,y,zk=x,y,z
From your result, justify why the radio-frequency must be applied perpendicular to the static magnetic field