Energy difference between spin up and spin down states
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The hydrogen atom is formed by one proton and one orbiting electron. Because the atomic number is 1, it has a spin quantum number 1/2. Hence, the hydrogen proton can exist in two spin states: 'up' state and 'down' state.
The hydrogen proton has a positive charge and can also generate magnetic dipole moments. When a magnetic field is applied to a proton dipole, the dipole will either align 'parallel' or 'anti-parallel' relative to the direction of the magnetic field depending on its spin state.
The 'parallel' (low energy) and 'anti-parallel' (high energy) states have a difference in energy (ΔE) proportional to the magnetic field strength (B0), gyromagnetic ratio (γ), and Planck constant (h):
- ΔE = γ * B0 * h / (2 * π)
Boltzmann statistics can describe the ratio of the number of nuclei in the high (Nhigh)and) and low (Nlow) energy states within a system as a function of the energy level difference (ΔE), temperature (T), and Boltzmann constant (k):
- Nhigh / Nlow = e - ΔE / (k * T)
-<p>The hydrogen atom is formed by one proton and one orbiting electron. Because the atomic number is 1, it has a spin quantum number 1/2. Hence, the hydrogen proton can exist in two spin states: 'up' state and 'down' state.</p><p>The hydrogen proton has a positive charge and can also generate magnetic dipole moments. When a magnetic field is applied to a proton dipole, the dipole will either <a href="/articles/net-magnetisation-vector">align 'parallel' or 'anti-parallel'</a> relative to the direction of the magnetic field depending on its spin state.</p><p>The 'parallel' (low energy) and 'anti-parallel' (high energy) states have a difference in energy (ΔE) proportional to the <a href="/articles/b0-1">magnetic field strength</a> (B<sub>0</sub>), <a href="/articles/gyromagnetic-ratio">gyromagnetic ratio</a> (γ), and Planck constant (h):</p><ul><li>ΔE = γ * B<sub>0</sub> * h / (2 * π)</li></ul><p>Boltzmann statistics can describe the ratio of the number of nuclei in the high (N<sub>high</sub>)and low (N<sub>low</sub>) energy states within a system as a function of the energy level difference (ΔE), temperature (T), and Boltzmann constant (k):</p><ul><li>N<sub>high</sub> / N<sub>low</sub> = e<sup> - ΔE / (k * T)</sup>- +<p>The hydrogen atom is formed by one proton and one orbiting electron. Because the atomic number is 1, it has a spin quantum number 1/2. Hence, the hydrogen proton can exist in two spin states: 'up' state and 'down' state.</p><p>The hydrogen proton has a positive charge and can also generate magnetic dipole moments. When a magnetic field is applied to a proton dipole, the dipole will either <a href="/articles/net-magnetisation-vector">align 'parallel' or 'anti-parallel'</a> relative to the direction of the magnetic field depending on its spin state.</p><p>The 'parallel' (low energy) and 'anti-parallel' (high energy) states have a difference in energy (ΔE) proportional to the <a href="/articles/b0-1">magnetic field strength</a> (B<sub>0</sub>), <a href="/articles/gyromagnetic-ratio">gyromagnetic ratio</a> (γ), and Planck constant (h):</p><ul><li>ΔE = γ * B<sub>0</sub> * h / (2 * π)</li></ul><p>Boltzmann statistics can describe the ratio of the number of nuclei in the high (N<sub>high</sub>) and low (N<sub>low</sub>) energy states within a system as a function of the energy level difference (ΔE), temperature (T), and Boltzmann constant (k):</p><ul><li>N<sub>high</sub> / N<sub>low</sub> = e<sup> - ΔE / (k * T)</sup>
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