4- The Nuclear Atom Flashcards
dispersion
Newton discovered a rainbow-colored band, aka “spectrum”
three general kinds of spectra
continuous
band
line
continuous spectra
emitted mainly by incandescent solids
show no lines at all
band spectra
very closely packed groups of lines that appear to be continuous in instruments of low-resolving power.
small solids placed in source flame / electrode
line spectra
arise from unbounded chemical elements
characteristic of individual elements or chemical compounds when excited under specific conditions
theoretical problem arising out of line spectra
classical physics could account for the existence of a continuous spectrum
classical physics could not explain why sharp lines and bands should exist
Balmer series
n ≥ 3 to n=2
Lyamn Series
n ≥ 2 to n=1
Paschen Series
n ≥ 4 to n=3
Rutherford and students (Geiger and Marsden)
- radiation from uranium consisted of at least 2 types, α and β
- suspected α must be doubly-ionized helium since q/m for α was half that of a p+
Rutherford atomic model experiment
let a radioactive substance, α, decay in a previously evacuated chamber; then, by spectroscopy, they detected the spectral lines of ordinary helium gas in the chamber.
used α to “feel about” within the interiors of other atoms.
Rutherford atomic model experiment interesting results
when a beam of α particles fell on a zinc sulfide screen (foil), visible light scintillations were observed.
most α particles went undeflected or deflected through small angles about 1°
unexpectedly, a few particles were deflected through angles as large as 90°
implications of the Rutherford atomic model experiment
If an atom consisted of a positively charged sphere of radius 1e-10, containing electrons as in the Thomson model, only a very small deflection would result from a single encounter.
Positive charge must be “concentrated” in the atom, with volume much smaller than entire atom.
why Rutherford results in conflict with the Thompson experiment…
Thomson atom is too soft–the maximum force experienced by the α is too weak to give a large deflection.
assumptions made for Rutherford scattering geometry equatin
final speed = initial speed
(through conservation of energy and the fact that potential = 0 after “collision’)
massive nucleus remains fixed during scatterng
smaller impact parameter (b) leads to a larger…
…scattering angle.
in Rutherfords experiment the nucleus is assumed to be a mathematical point charge. how is this different from reality?
as long as the particle did not penetrate the nucleus we can treat the nucleus as a point charge, mathematically.
to reduce the distance of closest approach, Rutherford…
did not have access to higher-energy α particles.
instead, used targets of smaller atomic numbers, then reduced the α particle’s KE by passing them through thin mica sheets of various thicknesses.
short wavelength
high frequency
high energy
long wavelength
low frequency
low energy
define “quantum”
minimum, indivisible amount of any physical entity or interaction
value of
hc
1240 eV⋄nm
series limit
when λ –> infinity
electron escapes at this point
Bohr assumptions
electrons exist in circular orbits without radiating
Bohr postulates
electrons can exist in stationary states (thus, no emissions)
atoms emit energy as a result of an electron jumping from higher to lower orbits. conversely, atoms absorb energy and an electron is promoted to higher orbit.
correspondence principle: in the limits of high energy or large orbitals (large n), we expect classical mechanics to “take over” and accurately predict behavior.
Bohr’s contributions
electrons exist in quantized orbitals (non-radiative)
jumps a result of/cause radiation
electrons have quantized angular momentum
this fell out of the math; beginning of quantum mechanics
lead to predictions that could be measured/tested
what does classical mechanics predict the electron will do
orbit around the nucleus, getting closer and closer (and faster) until, eventually, electron “crashes” into the nucleus. All the while, the atom is radiating energy.
this cannot be true because the atom would radiate a continuous spectrum.
Bohr frequency condition
hf = E(f) - E(i)
E(0) for hydrogen atom
n=1, “ground state”
- 6 eV
* n=1 but E(0)*
Balmer series in the ______ portion of the electromagnetic spectrum
visible
Lyman series in the ______ portion of the electromagnetic spectrum
infrared
The assumption by Bohr that the nucleus is fixed is equivalent to assuming…
…that the nucleus has infinite mass.
fine structure constant
Δn≥1 exist for small n. by correspondence principle, this should also be allowed for very large n. this adds major discrepancy to the correspondence principle b/c then all frequencies would be integer multiples of some basic frequency by the Bohr model.
to do away with the discrepancy we can allow elliptical orbits (where energy of an orbiting particle only depends on major axis)
technically incorrect, more in chapter. 7
alpha valued at roughly 1/137
relativistic corrections o the mass of an electron
Sommerfeld introduced the idea in hopes of explaining observed fine structure of the hydrogen spectral lines.
highly eccentric orbits have larger corrections
h(bar)c
197.3 eV⋄nm
Moseley
Using methods of crystal spectrometry, Moseley measured the wavelengths of characteristic x-ray line spectra for about 40 different target elements.
Noted the x-ray line spectra varied in a regular way from element to element. This variance due to transitions of inner-most electrons (not the shell).
results of bombarding an atom with x-ray
leads to ejection of electrons in inner-most shells. photons will then be emitted corresponding to transitions of electrons in other orbits to fill the n=1 vacancy.
“K series”
Franck-Hertz experiment confirmed….
by direct measurement, Bohr’s hypothesis of energy quantization in atoms.
Franck Hertz experiment setup…
A small heater heats a cathode, causing electrons to be ejected and accelerated through a potential difference (grid with positive V(0) relative to the cathode).
Grid then Plate, plate at potential V(P)=V(0)-ΔV.
Some electrons pass through holes in a metal grid and can reach a 2nd plate, thereby contributing to the current, I, if they have sufficient kinetic energy to overcome the small back potential, ΔV.
Tube filled with low-pressure gas of element being studied.
If electron does not have sufficient energy to transfer ΔE to hydrogen electron in the n=1 orbit (grounds state) then the scattering will be elastic. If it does have at least ΔE in Kinetic Energy, an inelastic collision will occur in which ΔE is transferred to the n=1 electron, moving it to the n=2 orbit. The excited electron will relax and emit a photon of energy ΔE.
For hydrogen, Franck-Hertz
If eV(0) ≥ 10.2 eV the incoming electron can transfer its energy to the hydrogen atom, promoting the n=1 electron to n=2.
How the Franck-Hertz proved Bohr’s model
When viewed with spectrometer, emission lines are not seen until the potential difference provides enough kinetic energy to “promote” an electron. Any energy below the required electron promotion yields no emission lines. Therefore, the emissions must be quantized.
Fraunhaffer
absorption emission lines
led to spectroscopy
if there are no dip-dip transitions allowed…
phosphorescence
in double slit, what are electrons interfering with?
itself
