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

Ionization Energy

2.17810J/a+m18(1nf21ni2)-2.178\cdot 10^{-18}_{J/a+m}\left ( \frac{1}{{n_{f}}^{2}}-\frac{1}{{n_{i}}^{2}} \right )

1312KJmol(1nf21ni2)\underline{-1312 \frac{KJ}{mol}\left ( \frac{1}{{n_{f}}^{2}}-\frac{1}{{n_{i}}^{2}} \right )}

E=z2e4m8εo2n2h2E=\frac{-z^{2}e^{4}m}{8{\varepsilon _{o}}^{2}n^{2}h^{2}} (negative because of the ee^{-} )

r=εon2h2ze2πmr=\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 ee^{-}

De Broglie

Light - Photons

  1. Plank - E=hVE=hV
  2. Einstein - E=mc2E=mc^{2}

hV=hcλ=mc2hV=\frac{hc}{\lambda }=mc^{2}

nλ=mc\frac{n}{\lambda }= mc

C - Velocity of light


  1. Standing wave nλ=2πrn\lambda = 2\pi r
  2. Bohr - mvr=nh2πmvr = \frac{nh}{2\pi }

2πr=nλ=nhmv2\pi r = n\lambda =\frac{nh}{mv}

nλ=mv\frac{n}{\lambda }=mv λ\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

ΔXΔPH4π\Delta X\cdot \Delta P\geq \frac{H}{4\pi }

ΔXmΔuH4π\Delta X\cdot m\Delta u \geq \frac{H}{4\pi }

ΔX:\Delta X : Uncertainty in position

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

Δu:\Delta u:  Change in velocity

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