Zeeman effect:z-component of spin angular momentum:z-component of the angular momentum:the effect of external magnetic fields on spectral linescomponent of intrinsic electron spin along thez-axis
component of orbital angular momentum of electron along thez-axis
Section Summary
30.1 Discovery of the Atom
- Atoms are the smallest unit of elements; atoms combine to form molecules, the smallest unit of compounds.
- The first direct observation of atoms was in Brownian motion.
• Analysis of Brownian motion gave accurate sizes for atoms ( 10 −10mon average) and a precise value for Avogadro’s number.
30.2 Discovery of the Parts of the Atom: Electrons and Nuclei
- Atoms are composed of negatively charged electrons, first proved to exist in cathode-ray-tube experiments, and a positively charged nucleus.
- All electrons are identical and have a charge-to-mass ratio of
qe
me= − 1.76×10
(^11) C/kg.
- The positive charge in the nuclei is carried by particles called protons, which have a charge-to-mass ratio of
qp
mp= 9.^57 ×10
(^7) C/kg.
- Mass of electron,
me= 9.11×10 −31kg.
- Mass of proton,
mp= 1.67×10 −27kg.
- The planetary model of the atom pictures electrons orbiting the nucleus in the same way that planets orbit the sun.
30.3 Bohr’s Theory of the Hydrogen Atom
- The planetary model of the atom pictures electrons orbiting the nucleus in the way that planets orbit the sun. Bohr used the planetary model to
develop the first reasonable theory of hydrogen, the simplest atom. Atomic and molecular spectra are quantized, with hydrogen spectrum
wavelengths given by the formula
1
λ
=R
⎛
⎝
⎜^1
nf^2
−^1
ni^2
⎞
⎠
⎟,
whereλis the wavelength of the emitted EM radiation andRis the Rydberg constant, which has the value
R= 1.097×10^7 m−1.
• The constantsniandnfare positive integers, andnimust be greater thannf.
- Bohr correctly proposed that the energy and radii of the orbits of electrons in atoms are quantized, with energy for transitions between orbits
given by
ΔE=hf=Ei−Ef,
whereΔEis the change in energy between the initial and final orbits andhf is the energy of an absorbed or emitted photon. It is useful to
plot orbital energies on a vertical graph called an energy-level diagram.- Bohr proposed that the allowed orbits are circular and must have quantized orbital angular momentum given by
L=mevrn=nh
2 π
(n= 1, 2, 3 ...),
whereLis the angular momentum,rnis the radius of thenthorbit, andhis Planck’s constant. For all one-electron (hydrogen-like) atoms,
the radius of an orbit is given byrn=n
2
Z
aB(allowed orbitsn= 1, 2, 3, ...),
Zis the atomic number of an element (the number of electrons is has when neutral) andaBis defined to be the Bohr radius, which is
aB= h
2
4 π^2 mekqe^2
= 0.529×10−10m.
- Furthermore, the energies of hydrogen-like atoms are given by
En= −Z
2
n^2
E 0 (n= 1, 2, 3 ...),
whereE 0 is the ground-state energy and is given by
E 0 =
2π^2 qe^4 mek^2
h^2
= 13.6 eV.
Thus, for hydrogen,1104 CHAPTER 30 | ATOMIC PHYSICS
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