Structure of Atom

Bohr's model solved the instability problem by proving about stationary states. In such stats, the electrons move in fixed orbits. They do not emit energy. This contradicted classical electromagnetic theory of Maxwell, which says accelerating charges should emit radiation and collapse into the nucleus. Bohr simply assumed Maxwell's laws don't apply to these special orbits.

Bohr's model is too simple for atoms beyond hydrogen. In multi-electron atoms like helium, it fails because it ignores a couple of aspects. First is the electron-to-electron repulsion, and second is the shielding effect, where inner electrons reduce the nuclear pull on outer ones. Due to both, orbitals with the same principal quantum number don't have the same energy. Bohr's model of atom assumes that it should have the same energy.

Radial node = n $\mathcal{l}-$ 1 (5d)

= 5 – 2 – 1 = 2

Angular node = $\mathcal{l}$

= 2

Correctly identifying isotopes and isobars requires knowing both the atomic and mass numbers. Relying on only one is a common error.

• Isotopes: Same element (atomic number), different mass.
• Isobars: Different elements (atomic number), same mass.

Rutherford's atomic model was a breakthrough, but it was flawed. It couldn't explain atomic stability, as orbiting electrons should lose energy and spiral into the nucleus. It also failed to account for the discrete line spectra observed from excited atoms.

According to Bohr's theory,

$K.E.=13.6\frac{z^2}{n^2}$ frequency $\left(\upsilon \right)$ of revolution of electron $\propto \frac{z^2}{n^3}$

  $v=2.18*10^6\frac{z}{n}$          

$F=\frac{k{q}_1{q}_2}{r^2}=\frac{Kz{e}^2}{r^2}\left(r\propto \frac{n^2}{z}\right)$       

$F\propto \frac{z^3}{n^4}$         

$E=\frac{hc}{\lambda }=\left\{\frac{6.63*10^{-34}*3*10^8}{663*10^{-9}}\right\}$

= 0.03 * 10^-17 = 3.0 * 10^-19 J/atom

= 18.06 * 10¹ kJ/mole = 180.6 181 KJ/mole

For 3S number of radial nodes are

= $n-\mathcal{l}-1=3-0-1=2$

The early 20th century experiments on electrical discharge through gases eventually led to the discovery of cathode rays (electrons). The major finding was that the characteristics of these cathode rays (electrons) were independent of the material used for the electrodes and the nature of the gas present in the cathode ray tube. This consistent behaviour across different substances led to the conclusion that electrons are a basic constituent of all atoms.