# 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 ﻿$e^{-}$﻿ )

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

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

### De Broglie

#### Light - Photons

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

﻿$hV=\frac{hc}{\lambda }=mc^{2}$﻿

﻿$\frac{n}{\lambda }= mc$﻿

C - Velocity of light

#### Electrons

1. Standing wave ﻿$n\lambda = 2\pi r$﻿
2. 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