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Energy of Hydrogen Like Atom Formula
On the Energy Formula of Hydrogen-like Atoms
The energy formula of a hydrogen atom is the key to physical research. Although it is not the original appearance of a hydrogen atom, its structure is similar to that of a hydrogen atom, with only one electron moving around the nucleus. The construction of this model provides a shortcut for understanding the mysteries of atoms.
The energy formula of hydrogen-like atoms is related to atomic structure, spectroscopy and many other fields. Its expression is usually $E_n = -\ frac {13.6Z ^ {2}} {n ^ {2}} eV $, where $Z $is the nuclear charge of the atom, $n $is the main quantum number, $n = 1,2,3,\ cdots $. This formula shows that the energy of hydrogen-like atoms is not continuously variable, but is quantized.
In principle, this formula is derived from the theory of quantum mechanics and the Bohr atomic model. Bohr assumed that electrons move in specific orbits, and the orbital energy is quantized. When electrons jump between different orbits, they will absorb or emit photons, and the photon energy is exactly equal to the difference between the two orbital energies. Based on this, combined with Coulomb's law and quantization conditions, the hydrogen-like atomic energy formula is derived.
In practical applications, in the field of spectroscopy, the position and intensity of the spectral lines of hydrogen-like atoms can be accurately predicted according to this formula. For example, when an electron jumps from a high energy level $n_2 $to a low energy level $n_1 $, the energy of the emitted photon is $\ Delta E = E_ {n_2} - E_ {n_1} $, and the photon frequency is obtained $\ nu =\ frac {\ Delta E} {h} $, which is an important basis for analyzing atomic spectra.
Furthermore, in atomic physics research, this formula helps to understand the properties of atomic stability, ionization energy, etc. Ionization energy is also the minimum energy required to free electrons from atomic bondage. According to the hydrogen-like atomic energy formula, when $n\ rightarrow\ infty $, $E_ {\ infty} = 0 $, then the energy required to ionize the electron from the ground state $n = 1 $is $E_ {\ infty} - E_1 = 13.6Z ^ {2} eV $.
In summary, the hydrogen-like atomic energy formula plays an important role in physics, and it has been fruitful in theoretical derivation and practical application. It has made great contributions to exploring the mysteries of atoms in the microscopic world and guided researchers to continue to delve into the unknown field of atomic physics.
The energy formula of a hydrogen atom is the key to physical research. Although it is not the original appearance of a hydrogen atom, its structure is similar to that of a hydrogen atom, with only one electron moving around the nucleus. The construction of this model provides a shortcut for understanding the mysteries of atoms.
The energy formula of hydrogen-like atoms is related to atomic structure, spectroscopy and many other fields. Its expression is usually $E_n = -\ frac {13.6Z ^ {2}} {n ^ {2}} eV $, where $Z $is the nuclear charge of the atom, $n $is the main quantum number, $n = 1,2,3,\ cdots $. This formula shows that the energy of hydrogen-like atoms is not continuously variable, but is quantized.
In principle, this formula is derived from the theory of quantum mechanics and the Bohr atomic model. Bohr assumed that electrons move in specific orbits, and the orbital energy is quantized. When electrons jump between different orbits, they will absorb or emit photons, and the photon energy is exactly equal to the difference between the two orbital energies. Based on this, combined with Coulomb's law and quantization conditions, the hydrogen-like atomic energy formula is derived.
In practical applications, in the field of spectroscopy, the position and intensity of the spectral lines of hydrogen-like atoms can be accurately predicted according to this formula. For example, when an electron jumps from a high energy level $n_2 $to a low energy level $n_1 $, the energy of the emitted photon is $\ Delta E = E_ {n_2} - E_ {n_1} $, and the photon frequency is obtained $\ nu =\ frac {\ Delta E} {h} $, which is an important basis for analyzing atomic spectra.
Furthermore, in atomic physics research, this formula helps to understand the properties of atomic stability, ionization energy, etc. Ionization energy is also the minimum energy required to free electrons from atomic bondage. According to the hydrogen-like atomic energy formula, when $n\ rightarrow\ infty $, $E_ {\ infty} = 0 $, then the energy required to ionize the electron from the ground state $n = 1 $is $E_ {\ infty} - E_1 = 13.6Z ^ {2} eV $.
In summary, the hydrogen-like atomic energy formula plays an important role in physics, and it has been fruitful in theoretical derivation and practical application. It has made great contributions to exploring the mysteries of atoms in the microscopic world and guided researchers to continue to delve into the unknown field of atomic physics.
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