# Lecture 8: Ionization Energy, Bohr's Theory, and Heisenberg's Uncertainty Principle,

### Ionization Energy

$-2.178\cdot 10^{-18}_{J/a+m}\left ( \frac{1}{{n_{f}}^{2}}-\frac{1}{{n_{i}}^{2}} \right )$

$\underline{-1312 \frac{KJ}{mol}\left ( \frac{1}{{n_{f}}^{2}}-\frac{1}{{n_{i}}^{2}} \right )}$

$E=\frac{-z^{2}e^{4}m}{8{\varepsilon _{o}}^{2}n^{2}h^{2}}$ (negative because of the $e^{-}$ )

$r=\frac{\varepsilon _{o}n^{2}h^{2}}{ze^{2}\pi m }$

(multiplied by Avogadro's number)

- Negative sign is the energy of the e
- Positive - to remove the $e^{-}$

### De Broglie

#### Light - Photons

**Plank**- $E=hV$**Einstein**- $E=mc^{2}$

$hV=\frac{hc}{\lambda }=mc^{2}$

$\frac{n}{\lambda }= mc$

**C - Velocity of light**

#### Electrons

- Standing wave $n\lambda = 2\pi r$
- Bohr - $mvr = \frac{nh}{2\pi }$

$2\pi r = n\lambda =\frac{nh}{mv}$

$\frac{n}{\lambda }=mv$ $\lambda$ is called **de Broglie's wavelength**

**V - Velocity of electron**

### Bohr's Theory

- You see that as the value of n increases radius of the orbit increases
- As the value of n increases (level of orbit), E, the energy increases (it becomes less negative as n is in the denominator.) But it is smaller and smaller while n goes up (difference)
- The E is always negative
- The condition for us to see/feel an object moving as a wave is - wavelength =/> than the object itself.

### Heisenberg's Uncertainty Principle

It is not possible to know both the position and momentum of a moving particle accurately at the same time. The more accurately we know the speed the less accurate we know the position and vice versa.

**X **= Position

**u** = Speed

**P** = Momentum

$\Delta X\cdot \Delta P\geq \frac{H}{4\pi }$

$\Delta X\cdot m\Delta u \geq \frac{H}{4\pi }$

$\Delta X :$ Uncertainty in position

$\Delta P :$ Mass in the velocity (uncertainty in momentum)

$\Delta u:$ Change in velocity

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