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I am slightly confused about the fact that when we are considering, for example, magnetic resonance or electron transition between energy levels, we seemed to only consider the potential energy in high school level. My questions are that when in an atom after an electron absorbs a photon and gained energy, why does it have to go to a high potential level, why cannot it simply speed up or go to a lower level because isn't the potential energy independent of photon energy?

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NMR relies on the fact that a magnetic dipole in an external magnetic field has an energy that depends on its orientation:

Magnetic dipole

Classically the magnetic dipole can make any angle with the magnetic field lines and the energy varies continuously as a function of the angle. However for a quantised system the energy takes discrete values. For example for a spin $\tfrac{1}{2}$ dipole the dipole can only be aligned parallel or antiparallel to the field so the energy can take only two values.

NMR works because the nuclei have a magnetic dipole so they behave just like the magnet in the above diagram. Nuclei with spin $\tfrac{1}{2}$ align with or against the field, and transitions between these two states produce or emit photons with an energy equal to this energy difference. The NMR spectrometer detects the emission/absorption of these photons.

So for a spin $\tfrac{1}{2}$ nucleus the photon can't do anything except stimulate this transition. When you ask why cannot it simply speed up that isn't a meaningful question. The magnetic dipole of the nucleus has only two states and all it can do is transition between them.

Higher spin nuclei have more states, but in all cases all you are doing is flipping the magnetic dipole between the discrete energy states available to it.

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  • $\begingroup$ Sorry, but there is no significant energy transfer out of the sample during the recording of the FID. There is NO emission of photons. Never, ever. Check your Einstein coefficient. onlinelibrary.wiley.com/doi/abs/10.1002/… $\endgroup$ – Karl Sep 10 '19 at 20:19
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When you are considering the atomic system, the classical mechanics breaks down and the quantum mechanics is used to describe the system. In quantum mechanics, the energy level of the constituents is described by an operator called Hamiltonian. This operator measures the total energy of the particle rather than just the potential or kinetic energy.

The transitions that we talk about in an atom, is due to change in the state of the electron as the energy levels are discrete, unlike the classical world. Thus, when an electron is supplied with some energy, for example with a photon, the electron should occupy a higher energy state than its current state due to the conservation of energy. Therefore, the electron has no other choice but to 'jump' to a higher energy level.

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