# Lecture 7: Bohr's Model (Specific Orbits and Assumptions)

﻿$E=\frac{nc}{\lambda }$﻿

﻿$E=\frac{6.626\cdot 10^{-34}_{Js}\cdot 3\cdot 10^{8}_{m/s}}{3972\cdot 10^{-9}_{m}}=5.00 \cdot 10^{19}_{J}\Rightarrow -5.00\cdot 10^{19}_{J}$﻿

﻿$\Delta E=\frac{nc}{\lambda }$﻿

﻿$\frac{1}{\lambda }=$﻿ Rudbargs Constant ﻿$=cnR$﻿ ﻿$\nu =R(\frac{1}{{n_{f}}^{2}}-\frac{1}{{n_{i}}^{2}})$﻿

﻿$\Delta E = nc\cdot R(\frac{1}{{n_{f}}^{2}}-\frac{1}{{n_{i}}^{2}})$﻿

﻿$6.626\cdot 10^{-34}_{Js}\cdot 300\cdot 10^{8}_{m/s} \left ( \frac{1}{2^{2}} -\frac{1}{{n_{2}}^{2}} \right )\cdot {10967700_{m}}^{-1}$﻿

﻿$-5.00\cdot 10^{-10}_{J}=2.178\cdot 10^{-18}_{J}\left ( \frac{1}{2^{2}}-\frac{1}{{n_{i}}^{2}} \right )$﻿

﻿$n=7$﻿

### Bohrs Model - Specific Orbits

﻿$mvr=nh/2\pi (1)$﻿

mvr - Angular momentum of the radius

Angular momentum is guantized by different values like 1h/2﻿$\pi,$﻿ 2h/2﻿$\pi,$﻿ 3h/2﻿$\pi...$﻿

V - Speed

m - Mass

h - Planks constant

• The Angular movement is quantized. ﻿$mvr=nh/2\pi (1)$﻿

#### First Assumption:

Standing wave - wave that can persist, remains constant position.

#### Second Assumption:

﻿$2﻿ π r - n ﻿ λ$﻿ (2) circumference of the orbit

• Distance is multiple of the wavelength

The size of the orbit is the integral multiple of the wave length

• Should be integral multiple the wave length (n﻿$\lambda$﻿ ).

#### Combination of the two

﻿$nh/2﻿ π﻿ = mvr$﻿

﻿$n﻿ λ = 2﻿ π﻿ r$﻿

﻿$r = nh/2﻿﻿ π mv$﻿

﻿$n﻿ λ ﻿ = 2﻿ π ﻿ ﻿ ⋅ ﻿ nh/2﻿ π mv$﻿ ﻿$\Rightarrow$﻿ ﻿$n﻿ λ﻿ = nh/mv$﻿ or ﻿$﻿ λ ﻿ = h/mv$﻿