Atomic Structure

Rutherford’s atomic model

$\text{Rutherford’s atomic model }$

$\to$ 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)

$\textbf{Findings}$

i) Outer hollow part – orbital or shell

ii) Central dense part – Nucleus

• 1 Fermi = 10^-15 m

$\textbf{Defects}$

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

$\text{Bohr’s atomic model or Bohr’s atomic theory}$

$\textbf{ Postulates}$

$\to$ 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, $∆E=E_2-E_1$

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

$n_2 \to n_1$ 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 $n_2=6,7,8….$

$\textbf{Notes}$: (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

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

The state and nature of electron in orbit.

Orbit Number	Orbit Designation	Principal Quantum Number(n)	Max. Number of Electrons in the orbit($2n^2$)
1	K	1	2
2	L	2	8
3	M	3	18
4	N	4	32
5	O	5	-
6	P	6	-

$\textbf{Principal Quantum Number}$

$\to$ 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 $∝ 1/n^2$

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

$\to$ 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

$n=3$

$l=0 …. (n-1)$

$= 0…..(3-1)$

$= 0,1,2$

$= s,p,d$

$\to$ Maximum no of electron in each subshell

$= 2(2l+1)$ or $4l+2$

$s= 4l+2=0+2=2=>$ (Sperical)

$p=4l+2=4+2=6=>$ (Dumbell)

$d=4l+2=8+2=10=>$ (Double dumbbell)

$f=4l+2=12+2=14=>$ ( Complicated )

$\to$ Azimuthal quantum number determines the shape of orbital.

$\to$ Orbital angular momentum $(mvr)=\dfrac{h}{2π} \sqrt{l(l+1)}$

$\textbf{Magnetic quantum number (m)}$

$\to$ Degenerated orbitals of each subshell.

$\to$ Orientation of orbitals in Zeeman effect

$\to$ Splitting of orbitals

$\to$ Represented by ‘m’

$\to$ Calculated by $m= 2l+1$

$\to$ M ranges from $–l$ to $+l$ including zero

i.e. $m = -l, 0, +l$

$\to$ Eg: For d sub shell:

$l=2$

no of orbitals of d-sub shell $(m) = 2l+1 = 2\times 2+1= 5$

$:. m = -l ,0,+l$

$= -2,-1,0,1,2$

$\textbf{Spin quantum number (s)}$

$\to$ The state and nature of electron in orbital

$\to$ Represented by ‘s’

$\to$Spin angular momentum $(mvr)=\dfrac{h}{2π} \sqrt{(s(s+1))}$

$\to$ Values are $+\dfrac{1}{2}$ and $-\dfrac{1}{2}$

Remember

$\text{Pauli’s exclusion principle}$

$\to$ No two electrons in an atom can have the same set of all quantum no.

$\to$ Eg: $Li=3=1s^2,2s^1=>$ Presence of Pauli’s exclusion principle

$Li=3=1s^3 =>$ Absence of Pauli’s Exclusion principle (Mistake)

$\textbf{Aufbau rule}$ or Simon’s (n+l) rule:

$\to$ an electron occupies orbitals in order from lowest energy to highest.

$\to$ $n+l$ rule

$\to$ $1s<2s<2p<3s<3p<4s<3d<…$

NOTE:

a) $4s<3d$

because for $4s=4+0=4$

For $3d=3+2=5$

$:. 4s(4) < 3d(5)$

b) $4p <5s$

Because $4p = 4+1 =5$

$5s =5+0 =5$

In this case electron must be filled in subshell with less principle quantum number.

$s<p<d<f$

$\textbf{Hund’s Rule of maximum multiplicity}$

$\to$ Electrons are filled in degenerated orbitals of each subshell at 1st single and then paired from lower energy level to higher energy level.

$\to$ Half filled and full filled orbitals are more stable

Eg : $p^2<p^3>p^4$ why? => (Half filled) Trigonal Planar

$\textbf{Note}$

$\to$ The compound of Zinc is always white because zinc has no unpaired electrons.

$\to$ $Cu^+$ is more stable than $Cu^{++}$ in solid state.

$\to$ $Cu^{++}$ is more stable than $Cu^{+}$ in solution state.

$\to$ $Fe^{+++}$ is more stable than $Fe^{++}$ in both solid and liquid state