Structure of Atom

$\mathrm{}\bar{v}=\frac{1}{\lambda }={\mathrm{R}\mathrm{z}}^2?\left(\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right)$

For $\mathrm{H}$ atom $\mathrm{z}=1$

$\bar{v}=R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$

For Balmer series:  ${\mathrm{n}}_1=2$

If ${\mathrm{n}}_2=3\therefore \frac{1}{\lambda }={\mathrm{R}\mathrm{z}}^2\left(\frac{1}{4}-\frac{1}{9}\right)$

$\frac{1}{\lambda }=\mathrm{R}\frac{5}{36}$

${\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}}=\frac{36}{5\mathrm{R}}$

In a hydrogen atom, which we know has a single electron, the orbital energy will only depend on the principal quantum number (n). Here, the orbitals like 2s and 2p have the same energy (degenerate).

It's a little different with multielectron atoms. The energy depends on both n and the azimuthal quantum number (l). This causes splitting. And, the energies increase in the order: s < p < d < f.

Total 25 orbitals are possible

Through Heisenberg's Uncertainty Principle, it's proven that you can't pin down where an electron is and how fast it's moving at the same time. The Bohr model did not look into this. The main reason for that thought was that it pictured electrons like little planets that would move in a loop around the nucleus. But that only works if you know both position and speed exactly. Nature doesn't let you do that. Add to it the fact that electrons also behave like waves, and the Bohr model just couldn't keep up. That's why scientists had to move on to the quantum model, which fits way better with how electrons actually act.

Δx . Δp = h/4π
Δx . mΔv = h/4π
Δv = 5 * 10? * 0.02/100 = 1000 m/s
∴ Δx = h/ (4πmΔv) = 6.63*10? ³? / (4*3.14*9.1*10? ³¹*1000)
= 5.8 * 10? m
= 58 * 10? m.

Rutherford atomic model can not explain hydrogen spectrum it is explained by Bohr's atomic model and from Bohr's atomic model, uncertainity principle can't be explained.

The existence of atomic spectra tells us that energy levels in atoms are quantised. When atoms absorb or emit light, they do so at specific wavelengths. They lead to line spectra instead of a continuous spectrum. Now, every line corresponds to an electron that transitions between fixed energy levels. This is to make the photon's energy equal to the difference between them. If energy levels were not discrete, the spectra would be continuous. So, the line spectra provide direct evidence that electrons in atoms occupy quantised energy states.