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Bohr’s model of H atom. PHY123. Niels Bohr (1885-1962). By Iutta Waloschek. Hydrogen atom. Positively charged nucleus inside ( +Ze ), negatively charged electron ( -e ) around Electron is attracted to nucleus Electron is trapped in a potential well created by nucleus (“a box”)

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bohr s model of h atom

Bohr’s model of H atom

PHY123

Lecture XIII

niels bohr 1885 1962
Niels Bohr (1885-1962)

Lecture XIII

By Iutta Waloschek

hydrogen atom
Hydrogen atom
  • Positively charged nucleus inside (+Ze), negatively charged electron (-e) around
  • Electron is attracted to nucleus
  • Electron is trapped in a potential well created by nucleus (“a box”)
  • Energy levels in atom

Lecture XIII

standing electron waves in hydrogen atom
Standing electron waves in Hydrogen atom
  • Standing waves:
  • 2prn=nl l=h/mv mvrn=nh/2p
  • Angular momentum L=mvrn is quantized

L=nh/2p

  • n – orbital quantum number

Lecture XIII

disclaimer
Disclaimer
  • Though Bohr’s model was able to predict many properties of H atom and correctly calculate some of its characteristics, this model is incomplete and it is not advisable to think of an atom as a miniature “solar system”.
  • Orbits make sense only as average radii of electron position (not the same as electron slightly smeared around circular orbits!!!)

Lecture XIII

hydrogen atom6
Hydrogen atom
  • mvrn=nh/2p v=nh/(2pmrn)
  • Newton’s 2nd law for circular motion:

Bohr radius

Lecture XIII

hydrogen atom7
Hydrogen atom
  • Energy in H atom KE+U

Lecture XIII

hydrogen atom8
Hydrogen atom
  • What did we learn?
  • For high n energy approaches -0, radius approaches infinity
  • Energy proportional to Z2e4
    • Ze2 from the potential, Ze2from 1/r (smaller orbits around larger charges)
  • Radius inversely proportional to mass (F=mv2/r)  Energy proportional to electron mass
  • Energy does not depend on nucleus mass – assume infinitely heavy
  • In classical case (h0) rn0 – electron falls on nucleus.

Lecture XIII

hydrogen atom9
Hydrogen atom
  • Energy levels in H
  • Infinite number of states n=1-infinity
  • All energies are negative – electron is trapped in atom
  • Lowest possible energy level E1=-13.6 eV – ground state
  • Positive energy – free electron –ionization
  • Ionization energy =13.6/n2for atom in n state

Lecture XIII

some parameters of the h atom
Some parameters of the H atom
  • Ground state n=1, Z=1
  • Electron’s “orbit” radius
  • Wavelength
  • Momentum
  • v/c

Lecture XIII

some parameters of the h atom11
Some parameters of the H atom
  • Ground state n=1, Z=1
  • Kinetic Energy
  • Potential Energy
  • Total energy
  • Longest wavelength absorbed (l – max E =hc/l – min)

n=1n=2

E1=-13.6eV E2=-13.6/4=-3.4eV Eg=13.6-3.4=10.2eV

l=hc/Eg=1243eVnm/10.2eV=122nm

Lecture XIII

a cute problem
A cute problem
  • Electrons are accelerated by 12.3V potential difference and pass through hydrogen gas at room T (ground state n=1). Which wavelengths of light can be observed?

Lecture XIII