Structure of Atom

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.

Before 20th century, atoms were widely considered the indivisible building blocks of matter. This view goes back to Indian and Greek philosophies, as old as 400 B.C. It also became one established thought on a scientific basis by John Dalton in 1808. With his theory, several fundamental laws of chemistry were established. But those laws failed against observations like static electricity. The experimental observations made towards the end of the 19th and beginning of the 20th century definitively proved that atoms are made of subatomic particles. 

$E_n=-R_H\left(\frac{Z^2}{n^2}\right)J$

For ${}^{+}\left(n=1\right)$ ,

$E_n=-x=-R_H\left(\frac{2^2}{1^2}\right)=-4R_H$

$\therefore R_H=\frac{x}{4}$

For ${}^{3+}\left(n=2\right)$ ,

$E_n=-R_H\left(\frac{z^2}{n^2}\right)J$

$=-\frac{x}{4}*\left(\frac{4*4}{2*2}\right)=-xJ$

Kindly go through the solution

Value of n &  $\mathcal{l}$ can't be same