## Rutherford’s atomic model

1. $\to$ Alpha ray

• Mechanical wave

• 2 +ve charge

• 2 protons + 2 neutrons

$\to$ Radioactive substance (Radium)

$\to$ Lead cavity

$\to$ Gold foil ( Thickness = 0.00004cm)

$\to$ ZnS Screen ( Alpha particle shines in ZnS screen)

$\to$ Nucleus ( As a Result)

2. $\textbf{Findings}$

i) Outer hollow part – orbital or shell

ii) Central dense part – Nucleus

• 1 Fermi = 10^-15 m

3. $\textbf{Defects}$

i) Does not explain continuous spectrum or H- spectrum

ii) The moving charge particle electron does not loss the energy (Does not follow law of electro dynamics)

## Bohr’s atomic model

1. $\textbf{ Postulates}$

$\to$ Stationary State: Energy neither loss nor gain when electron revolves round the nucleus is called stationary state.

$\to$ Quantization of angular momentum:

(Angular Momentum) $mvr=\dfrac{nh}{2π }$

$n=$Principle quantum no. $= 1,2,3,4...$ $= K,L,M,N…$

$hf=E_2-E_1$

$\dfrac{hc}{λ}=E_2-E_1$

$\to$ Formation of spectra: When we give energy externally, it jumps to the upper energy level and when it jumps to lower energy level, it emits energy in the form of spectra.

$E=hf$ (where $h=$ Plank’s constant and $f=$ frequency)

Similarly, $∆E=E_2-E_1$

2. $\textbf{Hydrogen Spectrum ( Emission spectrum ) }$

$n_2 \to n_1$ or $E_2 \to E_1$

i) Lyman Series:

• UV rays

• $n_1=1$ and $n_2=2,3,4….$

ii) Balmer Series:

• Visible region = observe photochemical Reaction

$= 3500-8000 \dot{A}$

= VIBGYOR

• $n_1=2$ and $n_2=3,4,5….$

iii) Paschen Series:

• IR

• $n_1=3$ and $n_2=4,5,6….$

iv) Brackett Series:

• IR

• $n_1=4$ and $n_2=5,6,7….$

v) Pfund Series:

• IR

• $n_1=5$ and $n_2=6,7,8….$

3. $\textbf{Notes}$: (Worth to remember)

$\to$ Total no of spectral lines $= \dfrac{n(n-1)}{2}$

$\to$ No of spectral lines in between two given series $=\dfrac{∆n (∆n+1)}{2}$

$\dfrac{1}{λ}=R(\dfrac{1}{n_1^2} -\dfrac{1}{n_2^2} ) =$ Balmer’s Formula

Where $R =$ Rydberg’s constant

4. Defects of Bohr’s atomic model:

i) It does not explain the micro or fine spectrum

ii) It does not explain the spectrum of multi electron system but only explain the spectrum of mono electron system like $H$$He^+$$Li^{++}$, etc.

iii) It does not explain the Zeeman effect (splitting of lines due to magnetic field), Stark effect ( Splitting of lines due to electric field) and Shielding effect.

iv) It does not explain the duel nature of electron

## Quantum Number

1. The state and nature of electron in orbit.

Orbit NumberOrbit DesignationPrincipal Quantum Number(n)Max. Number of Electrons in the orbit($2n^2$)
1K12
2L28
3M318
4N432
5O5-
6P6-
2. $\textbf{Principal Quantum Number}$

$\to$ Main shell or main orbit or main axis

$\to$ Represented by n

$n=1, 2, 3, 4…. =K, L, M, N….$ $\to$ It determines the size of atom

$\to$ Total no. of electron in each orbit $= 2n^2$

$\to$ Total no. of orbital in each orbit $= n^2$

Eg : L = 2s (s) , 2p ( px, py, pz)

$= 2^2$

$= 4$

$\to$ Also, radius $∝ n^2$

Energy $∝ 1/n^2$

3. $\textbf{Azimuthal quantum number (l)}$

$\to$ Sub shell or subsidiary or auxillary quantum number

$\to$Represented by ‘l’

$l = 0,1,2,3…(n-1)$ {1 less than principle quantum no.}

$= s,p,d,f…..$

$\to$ Eg: For K shell

$n=1$

$l=0 …. (n-1)$

$= 0…..(1-1)$

$= 0 =>$ s-sub shell

$\to$For M shell

$n=3$

$l=0 …. (n-1)$

$= 0…..(3-1)$