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

E=ncλE=\frac{nc}{\lambda }

E=6.62610Js34310m/s8397210m9=5.0010J195.0010J19E=\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}

ΔE=ncλ\Delta E=\frac{nc}{\lambda }

1λ=\frac{1}{\lambda }= Rudbargs Constant =cnR=cnR ν=R(1nf21ni2)\nu =R(\frac{1}{{n_{f}}^{2}}-\frac{1}{{n_{i}}^{2}})

ΔE=ncR(1nf21ni2)\Delta E = nc\cdot R(\frac{1}{{n_{f}}^{2}}-\frac{1}{{n_{i}}^{2}})

6.62610Js3430010m/s8(1221n22)10967700m16.626\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}

5.0010J10=2.17810J18(1221ni2)-5.00\cdot 10^{-10}_{J}=2.178\cdot 10^{-18}_{J}\left ( \frac{1}{2^{2}}-\frac{1}{{n_{i}}^{2}} \right )

n=7n=7


Bohrs Model - Specific Orbits

mvr=nh/2π(1)mvr=nh/2\pi (1)

mvr - Angular momentum of the radius

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

V - Speed

r - Radius of orbit

m - Mass

h - Planks constant

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


First Assumption:

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


Second Assumption:

2πrnλ2 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 (nλ\lambda ).


Combination of the two

nh/2π=mvrnh/2 π = mvr

nλ=2πrn λ = 2 π r

r=nh/2πmvr = nh/2 π mv

nλ=2πnh/2πmvn λ  = 2 π   ⋅  nh/2 π mv \Rightarrow nλ=nh/mv n λ = nh/mv  or λ=h/mv  λ  = h/mv


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