Physics Vidyapith ✍️

Although Bohr's model of hydrogen atom and hyarogen like atom was successful in explaining the stability and spectrum even then it has few limitations. which are as follows: (1) This model could not explain the spectrum of atom having more than one electron. (2) This model could not explain the relative intensity of spectral lines. (i. e., few transitions are more acceptable than others why?) (3) When a spectral line is observed by spectroscope of high resolution power, more than one lines are observed. This is known as fine structure of spectral line. Bohr model could not explain this. (4) Splitting of spectral lines in external magnetic field (Zeeman's effect) and in external electric field (Stark's effect) could not be explained by this model. (5) This model could not explain the distribution of electrons in different orbit. Few limitations of Bohr's model are removed in Somer-field's model of atom. (In this model, the orbit of electron was

A hydrogen-like atom consists of a very small positively-charged nucleus and an electron revolving in a stable circular orbit around the nucleus. The radius of electrons in stationary orbits: Let the charge, mass, velocity of the electron and the radius of the orbit is respectively  $e$, $m$, and $v$  and $r$. The $+ze$ is the positive charge on the nucleus where $Z$ is the atomic number of the atom. As We know that when an electron revolves around the nucleus then the centripetal force on an electron is provided by the electrostatic force of attraction between the nucleus and an electron, we have $\frac{mv^{2}}{r}=\frac{1}{4 \pi \epsilon_{\circ}} \frac{(Ze)(e)}{r^{2}}$ $mv^{2}=\frac{Ze^{2}}{4 \pi \epsilon_{\circ} r} \qquad(1)$ According to the first postulate of Bohr's model of the atom, the angular momentum of the electron is $mvr=n \frac{h}{2 \pi} \qquad(2)$ Where $n \: (=1,2,3,.....)$ is quantum number. Now squaring equation $(2)$ and dividi

Bohr's Atomic Model Postulates: Prof Neil in 1913 Bohr solve the difficulties of Ernest Rutherford's atomic model by applying Planck's quantum theory, For this, he proposed the following three Postulates: 1.) Electrons can revolve only in those orbits in which their angular momentum is an integral multiple of $\frac{h}{2 \pi}$. These orbits have discrete energy and definite radii. So it is called the " stable orbits ". If the mass of the electron is $m$ and it is revolving with velocity $v$ in an orbit of radius $r$, then its angular momentum will be $mvr$. According to Bohr's postulate, $mvr=\frac{nh}{2\pi}$ Where $h$ is Planck's universal constant This Bohr's equation is called the " Bohr's quantization Condition " 2.) When the electrons revolve in stable orbits then they do not radiate the energy in spite of their acceleration toward the center of the orbit. Hence atom remains stable and is said to exis