chemistry-class-11-unit-02-chapter-06-structure-of-the-atom-l-6-8-j0zdenlfp5y

### <Success style="font-size:25px"> Structure Of The Atom L-6 </Success>
### <primary style="font-size:24px"> Quantum number </primary>
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- Orientation of orbital (in space)
- Value for m depends of 'l' 
- Number of orientation
- l = 0 $\qquad\quad\quad$ (1)
- l = 1 $\qquad\quad\quad$ (3)
- l = 2 $\qquad\quad\quad$ (5)
- l = 3 $\qquad\quad\quad$ (7)

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<footer style = "font-size: 18px">Structure of atom $\rightarrow$ Quantum number $\rightarrow$ <span style = "color:blue"> Quantum number </span> $\rightarrow$ Quantum Number $\rightarrow$ Quantum number </footer>

### <Success style="font-size:25px"> Structure Of The Atom L-6 </Success>
### <primary style="font-size:24px"> Quantum number </primary>
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- $ \text{Total number of orientation} (2l+1)$ 
- $-l,-l+1,..0,..,l-1,+l$

| l | $(2l+1)$ | $m$ | Orbital          |
| --------  | -------- | -------- | -------- |
| 0    | 1     | 0               | s      |
| 1    | 3     | $-1,0,+1 $       |  $p_x ~ p_y ~ p_z$    </p>  |
| 2    | 5     | $-2,-1,0,+1,+2$  |  $d_{x y} ~ d_{y z} ~ d_{z x} ~ d_{x^2-y^2} ~ d_{z^2}$   |
| 3    | 7     | $-3,........,+3$  |     |

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<footer style = "font-size: 18px">Quantum number $\rightarrow$ Quantum Number $\rightarrow$ <span style = "color:blue"> Quantum number </span> $\rightarrow$ Examples $\rightarrow$ Examples </footer>

### <Success style="font-size:25px"> Structure Of The Atom L-6 </Success>
### <primary style="font-size:24px"> Summary </primary>
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| n       | l        | m          | $m_s$       |
| --------| -------- | --------   | --------    |
| size    | shape    | orientation| spin orientation |

- $n$ = $\quad$1, 2, 3, ..........

- $l$ = $\quad$0,1,2, .... n-1

- $m$ = $\quad -l,-l+1, \cdots  0, \cdots, l-1, l$

- $m_s$ = $\pm \frac{1}{2},-\frac{1}{2}$

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![image](https://temp-public-img-folder.s3.ap-south-1.amazonaws.com/sathee.prutor.images/subject-images/iitpal/image/chemistry-class-11-unit-02-chapter-06-structure-of-the-atom-l-6_8-j0zdenlfp5y-210-1111.2.jpg)

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<footer style = "font-size: 18px">Examples $\rightarrow$ Spin quantum number $\rightarrow$ <span style = "color:blue"> Summary </span> $\rightarrow$ Schrodinger equation $\rightarrow$ Angular nodes </footer>

### <Success style="font-size:25px"> Structure Of The Atom L-6 </Success>
### <primary style="font-size:24px"> Schrodinger equation </primary>
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- $H \psi=E \psi$
- $\psi \equiv \psi_{n l m}=\psi(n, l, m)$
- $\left|\psi_{n l  m}\right|^2=$ Probability density of the electron at a given point
- ${r(x, y, z)}$-$ \text { "spherical polar coordinates" } (r, \theta, \phi)$
- $\psi_{nlm} (r, \theta, \phi)$ = $R_{nl}$ (r) $\cdot Y_{lm} (\theta ,\phi)$ 
- ${R_{nl^{(r)}}}$-radial component (nl)$\rightarrow$ radial node
- ${Y_{nlm}(\theta ,\phi)}$ - angular component (lm) $\rightarrow$ angular node
- Node - region where probability of finding the electron is zero
- $\psi \rightarrow 0 (\psi)^2 $ = 0

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<footer style = "font-size: 18px">Spin quantum number $\rightarrow$ Summary $\rightarrow$ <span style = "color:blue"> Schrodinger equation </span> $\rightarrow$ Angular nodes $\rightarrow$ Radical nodes </footer>

### <Success style="font-size:25px"> Structure Of The Atom L-6 </Success>
### <primary style="font-size:24px"> Radical nodes </primary>
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<footer style = "font-size: 18px">Schrodinger equation $\rightarrow$ Angular nodes $\rightarrow$ <span style = "color:blue"> Radical nodes </span> $\rightarrow$ Radical nodes $\rightarrow$ Radical nodes </footer>

### <Success style="font-size:25px"> Structure Of The Atom L-6 </Success>
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- Radial nodes $R_{n l}(r)=0$
- Number of radial nodes
- $1s \rightarrow 0$
- $2 s \rightarrow 1$
- $3 s \rightarrow 2$
- $2 p \rightarrow 0$
- $3 p \rightarrow 1$

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<footer style = "font-size: 18px">Angular nodes $\rightarrow$ Radical nodes $\rightarrow$ <span style = "color:blue"> Radical nodes </span> $\rightarrow$ Radical nodes $\rightarrow$ Boundary surface diagrams </footer>

### <Success style="font-size:25px"> Structure Of The Atom L-6 </Success>
### <primary style="font-size:24px"> Boundary surface diagrams </primary>
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- 90% of the probability density should be accounted for

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<footer style = "font-size: 18px">Radical nodes $\rightarrow$ Boundary surface diagrams $\rightarrow$ <span style = "color:blue"> Boundary surface diagrams </span> $\rightarrow$ Energy of the orbitals $\rightarrow$ Energy of the orbitals </footer>

### <Success style="font-size:25px"> Structure Of The Atom L-6 </Success>
### <primary style="font-size:24px"> Energy of the orbitals </primary>
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- $\psi_{3 s}\rightarrow E_{3 s}$
- $\underbrace{(\psi_{3 p x} , \psi_{3 p y} , \psi_{3 p_z})}_ {E_{3p}}$
- $\underbrace{(E_{1S})}_ {1}$ < $\underbrace{( E_{2S} = E_{2px} = E_{2py} = E_{2pz})}_ {4}$ < $\underbrace{(E{3S} = E{3p} = E{3d})}_ {9}$
- 1,4,9 showing degenerated states

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<footer style = "font-size: 18px">Boundary surface diagrams $\rightarrow$ Energy of the orbitals $\rightarrow$ <span style = "color:blue"> Energy of the orbitals </span> $\rightarrow$ Energy of the orbitals $\rightarrow$ Thank you </footer>

### <Success style="font-size:25px"> Structure Of The Atom L-6 </Success>
### <primary style="font-size:24px"> Energy of the orbitals </primary>
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- **For multielectronic systems** 
- $\psi_{nlm} \quad E_{n l} \equiv$ depends on n & l
- $ 1s \quad 2s \quad 2p \quad 3s \quad 3p \quad 3d \quad 4s \quad 4p \quad 4 d \quad 4f$
- $n + l$ = $1 \quad 2 \quad 3 \quad 3 \quad 4 \quad 5 \quad 4 \quad 5 \quad 6 \quad 7$
- Energy increases with $n+l$
- $ E_{1s} < E_{2s} < E_{2p} < E_{3s} < E_{3p} < E_{4s} < E_{3d} < E_{4p} $

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<footer style = "font-size: 18px">Energy of the orbitals $\rightarrow$ Energy of the orbitals $\rightarrow$ <span style = "color:blue"> Energy of the orbitals </span> $\rightarrow$ Thank you $\rightarrow$  </footer>