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Quantum Numbers For Hydrogen
On the quantum number of hydrogen
The principle of things is subtle, and if you want to be infinite, you must explore its origin. Hydrogen is the beginning of elements, and the theory of its quantum number is crucial to the science of physics.
The quantum number of the hydrogen atom has the principal quantum number\ (n\), which is related to the energy of the electron and the orbital level.\ (n\) takes the value of a positive integer\ (1, 2, 3,\ cdots\). The larger the\ (n\), the higher the energy of the electron and the farther it is from the nucleus.
The angular quantum number\ (l\) is related to the orbital angular momentum of the electron. Its value is restricted by the principal quantum number,\ (l = 0, 1, 2,\ cdots, n - 1\). When\ (l = 0\), it is the\ (s\) orbital, which is spherically symmetric;\ (l = 1\) is the\ (p\) orbital, which is shaped like a dumbbell;\ (l = 2\) is the\ (d\) orbital, which is more complex. Different\ (l\) values represent the different shapes of the electron cloud.
Magnetic quantum number\ (m_l\), which determines the orientation of the orbital in space. Its value depends on the angular quantum number,\ (m_l = -l, -l + 1,\ cdots, l - 1, l\). For example, when\ (l = 1\),\ (m_l\) takes\ (-1,0,1\), indicating that the\ (p\) orbitals have three different orientations in space.
The spin quantum number\ (m_s\), which is related to the spin state of the electron, has only\ (+\ frac {1} {2}\) and\ (-\ frac {1} {2}\) binary values, indicating two opposite spin directions of the electron.
These four, the main quantum number\ (n\) fixed energy level, the angular quantum number\ (l\) fixed orbit shape, the magnetic quantum number\ (m_l\) fixed spatial orientation, and the spin quantum number\ (m_s\) fixed spin state. The collaboration of the four accurately depicts the state of electrons in hydrogen atoms, enabling us to understand the mysteries of the microscopic world. It has a profound impact on many fields of chemistry and physics, laying a solid foundation for the development of science.
The principle of things is subtle, and if you want to be infinite, you must explore its origin. Hydrogen is the beginning of elements, and the theory of its quantum number is crucial to the science of physics.
The quantum number of the hydrogen atom has the principal quantum number\ (n\), which is related to the energy of the electron and the orbital level.\ (n\) takes the value of a positive integer\ (1, 2, 3,\ cdots\). The larger the\ (n\), the higher the energy of the electron and the farther it is from the nucleus.
The angular quantum number\ (l\) is related to the orbital angular momentum of the electron. Its value is restricted by the principal quantum number,\ (l = 0, 1, 2,\ cdots, n - 1\). When\ (l = 0\), it is the\ (s\) orbital, which is spherically symmetric;\ (l = 1\) is the\ (p\) orbital, which is shaped like a dumbbell;\ (l = 2\) is the\ (d\) orbital, which is more complex. Different\ (l\) values represent the different shapes of the electron cloud.
Magnetic quantum number\ (m_l\), which determines the orientation of the orbital in space. Its value depends on the angular quantum number,\ (m_l = -l, -l + 1,\ cdots, l - 1, l\). For example, when\ (l = 1\),\ (m_l\) takes\ (-1,0,1\), indicating that the\ (p\) orbitals have three different orientations in space.
The spin quantum number\ (m_s\), which is related to the spin state of the electron, has only\ (+\ frac {1} {2}\) and\ (-\ frac {1} {2}\) binary values, indicating two opposite spin directions of the electron.
These four, the main quantum number\ (n\) fixed energy level, the angular quantum number\ (l\) fixed orbit shape, the magnetic quantum number\ (m_l\) fixed spatial orientation, and the spin quantum number\ (m_s\) fixed spin state. The collaboration of the four accurately depicts the state of electrons in hydrogen atoms, enabling us to understand the mysteries of the microscopic world. It has a profound impact on many fields of chemistry and physics, laying a solid foundation for the development of science.
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