4- The Nuclear Atom

Question 1

dispersion

Answer 1

Newton discovered a rainbow-colored band, aka “spectrum”

Question 2

three general kinds of spectra

Answer 2

continuous
band
line

Question 3

continuous spectra

Answer 3

emitted mainly by incandescent solids

show no lines at all

Question 4

band spectra

Answer 4

very closely packed groups of lines that appear to be continuous in instruments of low-resolving power.

small solids placed in source flame / electrode

Question 5

line spectra

Answer 5

arise from unbounded chemical elements

characteristic of individual elements or chemical compounds when excited under specific conditions

Question 6

theoretical problem arising out of line spectra

Answer 6

classical physics could account for the existence of a continuous spectrum

classical physics could not explain why sharp lines and bands should exist

Question 7

Balmer series

Answer 7

n ≥ 3 to n=2

Question 8

Lyamn Series

Answer 8

n ≥ 2 to n=1

Question 9

Paschen Series

Answer 9

n ≥ 4 to n=3

Question 10

Rutherford and students (Geiger and Marsden)

Answer 10

• 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+

Question 11

Rutherford atomic model experiment

Answer 11

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.

Question 12

Rutherford atomic model experiment interesting results

Answer 12

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°

Question 13

implications of the Rutherford atomic model experiment

Answer 13

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.

Question 14

why Rutherford results in conflict with the Thompson experiment…

Answer 14

Thomson atom is too soft–the maximum force experienced by the α is too weak to give a large deflection.

Question 15

assumptions made for Rutherford scattering geometry equatin

Answer 15

final speed = initial speed
(through conservation of energy and the fact that potential = 0 after “collision’)

massive nucleus remains fixed during scatterng

Question 16

smaller impact parameter (b) leads to a larger…

Answer 16

…scattering angle.

Question 17

in Rutherfords experiment the nucleus is assumed to be a mathematical point charge. how is this different from reality?

Answer 17

as long as the particle did not penetrate the nucleus we can treat the nucleus as a point charge, mathematically.

Question 18

to reduce the distance of closest approach, Rutherford…

Answer 18

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.

Question 19

short wavelength

Answer 19

high frequency

high energy

Question 20

long wavelength

Answer 20

low frequency

low energy

Question 21

define “quantum”

Answer 21

minimum, indivisible amount of any physical entity or interaction

Question 22

value of

hc

Answer 22

1240 eV⋄nm

Question 23

series limit

Answer 23

when λ –> infinity

electron escapes at this point

Question 24

Bohr assumptions

Answer 24

electrons exist in circular orbits without radiating

Question 25

Bohr postulates

Answer 25

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.

Question 26

Bohr’s contributions

Answer 26

electrons exist in quantized orbitals (non-radiative)

jumps a result of/cause radiation

Question 27

electrons have quantized angular momentum

Answer 27

this fell out of the math; beginning of quantum mechanics

lead to predictions that could be measured/tested

Question 28

what does classical mechanics predict the electron will do

Answer 28

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.

Question 29

Bohr frequency condition

Answer 29

hf = E(f) - E(i)

Question 30

E(0) for hydrogen atom

n=1, “ground state”

Answer 30

13. 6 eV

* n=1 but E(0)*

Question 31

Balmer series in the ______ portion of the electromagnetic spectrum

Answer 31

visible

Question 32

Lyman series in the ______ portion of the electromagnetic spectrum

Answer 32

infrared

Question 33

The assumption by Bohr that the nucleus is fixed is equivalent to assuming…

Answer 33

…that the nucleus has infinite mass.

Question 34

fine structure constant

Answer 34

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

Question 35

relativistic corrections o the mass of an electron

Answer 35

Sommerfeld introduced the idea in hopes of explaining observed fine structure of the hydrogen spectral lines.

highly eccentric orbits have larger corrections

Question 36

h(bar)c

Answer 36

197.3 eV⋄nm

Question 37

Moseley

Answer 37

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).

Question 38

results of bombarding an atom with x-ray

Answer 38

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”

Question 39

Franck-Hertz experiment confirmed….

Answer 39

by direct measurement, Bohr’s hypothesis of energy quantization in atoms.

Question 40

Franck Hertz experiment setup…

Answer 40

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.

Question 41

For hydrogen, Franck-Hertz

Answer 41

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.

Question 42

How the Franck-Hertz proved Bohr’s model

Answer 42

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.

Question 43

Fraunhaffer

Answer 43

absorption emission lines

led to spectroscopy

Question 44

if there are no dip-dip transitions allowed…

Answer 44

phosphorescence

Question 45

in double slit, what are electrons interfering with?

Answer 45

itself