Bohr Model Of Atom I
Bohr Model of Atom  I
Fundamental Postulates of Bohr’s Model
 Electrons orbit the nucleus in fixed circular paths of definite radii. These orbits are called stationary orbits or energy levels.
 Each orbit has a specific energy associated with it, and the electron can move from one orbit to another by absorbing or emitting a photon of light.
 The angular momentum of an electron in a given orbit is quantized, i.e., it can have only certain discrete values.
Explanation of Line Spectra of Hydrogen Atom Based on Bohr’s Model
 When an electron in a hydrogen atom transitions from a higher energy orbit to a lower energy orbit, it emits a photon of light with a wavelength that corresponds to the energy difference between the two orbits.
 The line spectra of hydrogen atom are the result of these specific transitions.
Calculation of Radius of Electron Orbits, Energy of Electron in Orbit, and Frequency of Emitted Radiation

The radius (r) of the nth orbit is given by: $$r_n = \left(\frac{4\pi\epsilon_0}{m_e}\right)n^2a_0$$

The energy (En) of an electron in the nth orbit is given by: $$E_n = \frac{1}{8 \pi \epsilon_0}\frac{e^2}{r_n} = \frac{1}{8\pi \epsilon_0}\frac{m_ek^2e^2}{4\pi \epsilon_0 n^2\hbar^2}$$ $$E_n = \frac{1}{n^2}\frac{m_ek^2e^2}{8h^2\epsilon_0}$$

The frequency (f) of the radiation emitted when an electron transitions from the nth orbit to the mth orbit is given by: $$f = \frac{\Delta E}{h} = \frac{E_n  E_m}{h}$$
Bohr’s Formula for Calculating Ionization Energy The ionization energy (IE) of an atom is the energy required to remove an electron from the atom’s lowest energy level (n=1). Bohr’s formula for ionization energy is: $$IE = E_1 = \frac{1}{8h^2\epsilon_0}\frac{m_ek^2e^2}{2^2}$$ $$IE = \frac{1}{8}\frac{m_ek^2e^2}{4h^2\epsilon_0}$$ $$IE = \frac{1}{8}\frac{(9.109\times10^{31}\text{ kg})(8.99\times10^9\text{ N}\cdot\text{m}^2/\text{C}^2)(1.602\times10^{19}\text{ C})^2}{4(6.626\times10^{34}\text{ J}\cdot\text{s})^2(8.85\times10^{12}\text{ C}^2/\text{N}\cdot\text{m}^2)}$$ $$IE = \frac{1}{8}(13.60569)\text{ eV} = 1.7 \text{ eV}$$
Limitations of Bohr’s Model
 Bohr’s model:
 Doesn’t explain the splitting of spectral lines observed in the presence of external magnetic fields (Zeeman effect) or electric fields (Stark effect).
 Doesn’t explain the fine structure of spectral lines, which is due to the spin of the electron.
 Can’t explain the chemical bonding between atoms.
Application of Bohr’s Model to Other Atoms and Ions Bohr’s model can be applied to other oneelectron atoms and ions such as He+ and Li2+, but it is less accurate for these larger atoms because of the increased number of electrons and electronelectron interactions.