What is bohr's law and describe it
Answers
Answered by
1
In atomic physics, the Rutherford–Bohr model or Bohr model or Bohr diagram, introduced by Niels Bohr and Ernest Rutherford in 1913, depicts the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the nucleus—similar to structure of the Solar System, but with attraction provided by electrostatic forces rather than gravity. After the cubic model (1902), the plum-pudding model (1904), the Saturnian model (1904), and the Rutherford model (1911) came the Rutherford–Bohr model or just Bohr model for short (1913). The improvement to the Rutherford model is mostly a quantum physical interpretation of it. The model's key success lay in explaining the Rydberg formulafor the spectral emission lines of atomic hydrogen. While the Rydberg formula had been known experimentally, it did not gain a theoretical underpinning until the Bohr model was introduced. Not only did the Bohr model explain the reason for the structure of the Rydberg formula, it also provided a justification for its empirical results in terms of fundamental physical constants.
The Bohr model is a relatively primitive model of the hydrogen atom, compared to the valence shell atom. As a theory, it can be derived as a first-order approximation of the hydrogen atom using the broader and much more accurate quantum mechanics and thus may be considered to be an obsolete scientific theory. However, because of its simplicity, and its correct results for selected systems (see below for application), the Bohr model is still commonly taught to introduce students to quantum mechanics or energy level diagrams before moving on to the more accurate, but more complex, valence shell atom. A related model was originally proposed by Arthur Erich Haas in 1910, but was rejected. The quantum theory of the period between Planck's discovery of the quantum (1900) and the advent of a full-blown quantum mechanics (1925) is often referred to as the old quantum theory.
The Rydberg formula, which was known empirically before Bohr's formula, is seen in Bohr's theory as describing the energies of transitions or quantum jumps between one orbital energy levels. Bohr's formula gives the numerical value of the already-known and measured Rydberg's constant, but in terms of more fundamental constants of nature, including the electron's charge and Planck's constant.
When the electron gets moved from its original energy level to a higher one, it then jumps back each level until it comes to the original position, which results in a photonbeing emitted. Using the derived formula for the different energy levels of hydrogen one may determine the wavelengths of light that a hydrogen atom can emit.
The energy of a photon emitted by a hydrogen atom is given by the difference of two hydrogen energy levels:
{\displaystyle E=E_{i}-E_{f}=R_{\mathrm {E} }\left({\frac {1}{n_{f}^{2}}}-{\frac {1}{n_{i}^{2}}}\right)\,}
where nf is the final energy level, and ni is the initial energy level.
Since the energy of a photon is
{\displaystyle E={\frac {hc}{\lambda }},\,}
the wavelength of the photon given off is given by
{\displaystyle {\frac {1}{\lambda }}=R\left({\frac {1}{n_{f}^{2}}}-{\frac {1}{n_{i}^{2}}}\right).\,}
This is known as the Rydberg formula, and the Rydberg constant R is RE/hc, or RE/2π in natural units. This formula was known in the nineteenth century to scientists studying spectroscopy, but there was no theoretical explanation for this form or a theoretical prediction for the value of R, until Bohr. In fact, Bohr's derivation of the Rydberg constant, as well as the concomitant agreement of Bohr's formula with experimentally observed spectral lines of the Lyman (nf =1), Balmer (nf =2), and Paschen (nf =3) series, and successful theoretical prediction of other lines not yet observed, was one reason that his model was immediately accepted.
To apply to atoms with more than one electron, the Rydberg formula can be modified by replacing Z with Z−b or n with n−b where bis constant representing a screening effect due to the inner-shell and other electrons (see Electron shell and the later discussion of the "Shell Model of the Atom" below). This was established empirically before Bohr presented his model.
The Bohr model is a relatively primitive model of the hydrogen atom, compared to the valence shell atom. As a theory, it can be derived as a first-order approximation of the hydrogen atom using the broader and much more accurate quantum mechanics and thus may be considered to be an obsolete scientific theory. However, because of its simplicity, and its correct results for selected systems (see below for application), the Bohr model is still commonly taught to introduce students to quantum mechanics or energy level diagrams before moving on to the more accurate, but more complex, valence shell atom. A related model was originally proposed by Arthur Erich Haas in 1910, but was rejected. The quantum theory of the period between Planck's discovery of the quantum (1900) and the advent of a full-blown quantum mechanics (1925) is often referred to as the old quantum theory.
The Rydberg formula, which was known empirically before Bohr's formula, is seen in Bohr's theory as describing the energies of transitions or quantum jumps between one orbital energy levels. Bohr's formula gives the numerical value of the already-known and measured Rydberg's constant, but in terms of more fundamental constants of nature, including the electron's charge and Planck's constant.
When the electron gets moved from its original energy level to a higher one, it then jumps back each level until it comes to the original position, which results in a photonbeing emitted. Using the derived formula for the different energy levels of hydrogen one may determine the wavelengths of light that a hydrogen atom can emit.
The energy of a photon emitted by a hydrogen atom is given by the difference of two hydrogen energy levels:
{\displaystyle E=E_{i}-E_{f}=R_{\mathrm {E} }\left({\frac {1}{n_{f}^{2}}}-{\frac {1}{n_{i}^{2}}}\right)\,}
where nf is the final energy level, and ni is the initial energy level.
Since the energy of a photon is
{\displaystyle E={\frac {hc}{\lambda }},\,}
the wavelength of the photon given off is given by
{\displaystyle {\frac {1}{\lambda }}=R\left({\frac {1}{n_{f}^{2}}}-{\frac {1}{n_{i}^{2}}}\right).\,}
This is known as the Rydberg formula, and the Rydberg constant R is RE/hc, or RE/2π in natural units. This formula was known in the nineteenth century to scientists studying spectroscopy, but there was no theoretical explanation for this form or a theoretical prediction for the value of R, until Bohr. In fact, Bohr's derivation of the Rydberg constant, as well as the concomitant agreement of Bohr's formula with experimentally observed spectral lines of the Lyman (nf =1), Balmer (nf =2), and Paschen (nf =3) series, and successful theoretical prediction of other lines not yet observed, was one reason that his model was immediately accepted.
To apply to atoms with more than one electron, the Rydberg formula can be modified by replacing Z with Z−b or n with n−b where bis constant representing a screening effect due to the inner-shell and other electrons (see Electron shell and the later discussion of the "Shell Model of the Atom" below). This was established empirically before Bohr presented his model.
Similar questions
Math,
7 months ago
English,
7 months ago
Math,
7 months ago
Math,
1 year ago
CBSE BOARD X,
1 year ago