chemistry-class-11-unit-02-chapter-05-structure-of-the-atom-l-5-8-zg2cps5wbus

### <Success style="font-size:25px"> Structure Of The Atom L-5 </Success>
### <primary style="font-size:24px"> Heisenberg's uncertainty principle </primary>
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- Simultaneous determination of exact position and exact momentum of a particle is impossible
 - $\Delta x$ uncertainty in position
 - $\Delta p_x$ uncertainty in momentum 
 - Uncertainty of an electron
 - $\Delta x \cdot \Delta p_x \geqslant \frac{h}{4 \pi} \Rightarrow \Delta x \cdot \Delta v \geqslant \frac{n}{4 \pi m}$
 - $\frac{6.626 \times 10^{-34} \mathrm{J} . \mathrm{s}}{4 \times 3.14 \times 9.1 \times 10^{-31} \mathrm{kg}}\approx 10^{-4} \mathrm{m}^2\mathrm{s}^{-1}$

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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-05-structure-of-the-atom-l-5_8-zg2cps5wbus-063-0368.4.jpg)

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<footer style = "font-size: 18px"> $\rightarrow$ Structure of the atom $\rightarrow$ <span style = "color:blue"> Heisenberg's uncertainty principle </span> $\rightarrow$ Uncertainty principle $\rightarrow$ Reason's for the failure of bohr's model </footer>

### <Success style="font-size:25px"> Structure Of The Atom L-5 </Success>
### <primary style="font-size:24px"> Uncertainty principle </primary>
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- $\Delta x {.} \Delta v_x$ $\approx$ $10^{-4} {m^2}s^{-1}$</P>
- $\Delta x {.} \Delta v_x \geqslant \frac{h}{4 \pi m} \$
- When m = 100 g 
- $\frac{6.626 \times 10^{-34} \mathrm{J} .5}{4 \times 3.14 \times 0.1 \mathrm{kg}} \approx 10^{-33} \mathrm{m}^2 \mathrm{s}^{-1}$

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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-05-structure-of-the-atom-l-5_8-zg2cps5wbus-087-0561.6.jpg)

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<footer style = "font-size: 18px">Structure of the atom $\rightarrow$ Heisenberg's uncertainty principle $\rightarrow$ <span style = "color:blue"> Uncertainty principle </span> $\rightarrow$ Reason's for the failure of bohr's model $\rightarrow$ Postulates of quantum mechanics </footer>

### <Success style="font-size:25px"> Structure Of The Atom L-5 </Success>
### <primary style="font-size:24px"> Postulates of quantum mechanics </primary>
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- **Wavefunction** $(\Psi,\psi)$
- Wavefunction can be
  - $x, x^2, \sin x, e^{-x}, e^{-i x}$, a+ib 
  - For every quantum mechanical system their exist a wavefuntion
  - $\Psi$ - does not have physical meaning

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<footer style = "font-size: 18px">Uncertainty principle $\rightarrow$ Reason's for the failure of bohr's model $\rightarrow$ <span style = "color:blue"> Postulates of quantum mechanics </span> $\rightarrow$ Postulates of quantum mechanics $\rightarrow$ Postulates of quantum mechanics </footer>

### <Success style="font-size:25px"> Structure Of The Atom L-5 </Success>
### <primary style="font-size:24px"> Postulates of quantum mechanics </primary>
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- **Wavefunction** $(\Psi,\psi)$
 - According to max born $|\psi|^2$ has physical meaning
 - Probability of finding electron at a given point in space $|\psi|^2$ is always positive 
 - $\psi=x \Rightarrow|\psi|^2=x^2 \$
 - $\psi =\left.e^{-x} \Rightarrow |\psi\right|^2=e^{-2 x}$
 - If $\psi\$ is complex function then $|\psi|^2=\Psi^*\Psi$ 
 - $\psi=a+i b \Rightarrow|\psi|^2=\Psi^*\Psi$  
 - $\psi=(a-i b)$ $(a+i b)=a^2+b^2$

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<footer style = "font-size: 18px">Reason's for the failure of bohr's model $\rightarrow$ Postulates of quantum mechanics $\rightarrow$ <span style = "color:blue"> Postulates of quantum mechanics </span> $\rightarrow$ Postulates of quantum mechanics $\rightarrow$ Postulates of quantum mechanics </footer>

### <Success style="font-size:25px"> Structure Of The Atom L-5 </Success>
### <primary style="font-size:24px"> Postulates of quantum mechanics </primary>
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- Results from the solution of schrödinger equation
- $H \psi=E \psi$
- A series of wavefunction $\equiv$ orbitals
- $\underbrace{\text{atomic orbitals}}_ {\text{"address of electron"}}$
- A series of energies ${\text {(discrete set)}}$
  - {0,5,10,15}
  - {0,10,16,29}

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<footer style = "font-size: 18px">Postulates of quantum mechanics $\rightarrow$ Postulates of quantum mechanics $\rightarrow$ <span style = "color:blue"> Postulates of quantum mechanics </span> $\rightarrow$ Orbitals $\rightarrow$ Orbitals </footer>

### <Success style="font-size:25px"> Structure Of The Atom L-5 </Success>
### <primary style="font-size:24px"> Orbitals </primary>
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- **Azimuthal Quantum Number**
- Orbital quantum number (l) it tells us about the "shape" of the orbital
- $l$ =  0,$\quad$ 1,$\quad$ 2, $\dots$ , n-1

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|          |           |           | l        |
| -------- | --------  | --------  | -------- |
|$n$ = 1   | l = 0     |           | 1        |
|$n$ = 2  | l = 0     | 1         | 2        |
|$n$ = 3  | l = 0     |1 $\quad$ 2| 3        |

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<footer style = "font-size: 18px">Orbitals $\rightarrow$ Orbitals $\rightarrow$ <span style = "color:blue"> Orbitals </span> $\rightarrow$ Shape $\rightarrow$ Shape </footer>

### <Success style="font-size:25px"> Structure Of The Atom L-5 </Success>
### <primary style="font-size:24px"> Shape </primary>
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- **Azimuthal Quantum Number**
 - Orbital quantum number (l)
 - "Shape" of the orbital
 - $l$ = $\quad$ 0,$\quad$ 1,$\quad$ 2, $\dots$ , n-1

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|          |           |                   |<p style="font-size:26px"> l </p>       |
| -------- | --------  | --------          | -------- |
|<p style="font-size:26px">n =1</p> |<p style="font-size:24px"> l = 0 (1S)</p>|    |<p style="font-size:26px"> 1 </p>       |
|<p style="font-size:24px">n = 2</p> |<p style="font-size:24px"> l = 0 (2S)</p> |<p style="font-size:26px"> 1 (2p) </p> |<p style="font-size:26px"> 2 </p> |
|<p style="font-size:24px">n = 3</p> |<p style="font-size:24px"> l = 0 (3S) </p>|<p style="font-size:24px">1 (3p)$\quad$ 2(3d)</p>|<p style="font-size:26px"> 3 </p> |

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<footer style = "font-size: 18px">Orbitals $\rightarrow$ Shape $\rightarrow$ <span style = "color:blue"> Shape </span> $\rightarrow$ Shape $\rightarrow$ Thank you </footer>