Transcript 1.2 The mass and size of the atom

1.2 The mass of the atom
With the methods of chemistry:
• Dalton’s law of constant and multiple proportions
The atomic weights are approximately whole-number
multiples of the atomic mass of the Hydrogen atom.
The atomic mass unit 1 u or 1 amu is defined as the mass of Hydrogen
The relative atomic masses: Arel(N)14, Arel(O)16
1961 standard: 1 u = 1/12 of the mass of 12C
To be expedient for the experimental precision determination of atomic masses by
chemical means
Compare: amu(H) : amu(12C) = 0.99996 : 1.00000
Avogadro’s hypothesis:
equal volumes of gas (at similar conditions:
pressure, temperature) contain the same number
of molecules or atoms.
Avogadro’s number NA: 1 mole of any substance
contains the same number (NA) of atoms.
The present value:
NA = (6.022045 ± 0.000005) × 1023 mole-1
The absolute atomic mass:
Matom = mass of 1 mole of the substance / NA
1 mole of 12C is 12 grams:
12 g / mol
m( C ) 
 19.92516 10  27 kg
NA
12
6
m(O)  26.5584 1027 kg
1 u = (12/12) grams / NA
= (1.660565 ± 0.000005) × 10-27 kg
= 931.478 MeV/c2
Determination of Avogadro’s number NA
• Electrolysis
In electrolytic decomposition of salts from a solution,
for 1 mole of a monovalent substance (for example
Cu+), a charge of 96485 As (Ampere-second) can
be required.
NA = F/e,
F: the Faraday constant, 96485 As/mole
e: the charge of a single electron
Other methods to determine the mass of atom:
• The gas constant R and Boltzmann’s
constant k, k = R/NA
• X-ray diffraction in Crystals
• Determination using radioactive Decay
• Mass spectroscopy
Mass spectroscopy — a physical method:
By determining the ratio of charge to
mass e/m, by the deflection of ionized
atoms moving through electronic and
magnetic fields.
The oldest and most easily understandable –
Parabola method by Thomson in 1913
Parabola method
oven
The ion beam, collimated by the slit S, is
deflected by the magnet M and the condenser C
in the x and y directions.
Separation of a mixture of
hydrocarbon. The orbit of deflected
particles on screen:
y
2E m 2
 x
2 2
l B e
Advantage of the Parabola method:
differing velocities due to their preparation in
an oven, those ions having the same value of
e/m on a same parabola
Improved types (higher resolution) and modern
applications:
a) with velocity focussing (by Aston 1919)
b) With directional focussing in a magnetic sector
field by Dempster in 1918
c) Double focussing – velocity and directional
focussing
d) Quadrupole mass spectroscopy
Quadrupole mass spectrometer
Schematic of a quadrupole mass filter. The ion beam, moving in the +z direction, is
deflected by a high-frequency alternating potential. In order for the beam to pass
through the filter, a certain relation between e/m, the frequency , and the deflection
voltages U and V must be fulfilled. The dashed orbit applies to an ion for which this
condition is not met.
1.3 the size of the atom
Methods in history:
 Application of the kinetic theory of gases
Using ideal-gas law: pV = nRT
 Determining the atom size from the
covolume of the Van der Waals equation in
a real gas states: (p+a/V2)(V-b) = RT
 The interaction cross-section
Mordern methods:
 Directly measured by Scanning
Tunneling Microscopy (STM), and
electron microscopy (SEM or TEM)
 X-ray diffraction measurement on
crystals
Incident
X-rays
1
Diffracted
x-rays
2
atoms
Incident
X-rays
Atomic planes
1
2
Diffracted
x-rays
Bragg (in 1913) interference condition:
1= 2 = 
With the X-ray path difference:
 = AB+BC-AE = n
2dsin = n
Practical methods of observing X-ray
diffraction:
• The Laue method: uses a single crystal, and
polychromatic X-ray
• The Bragg rotating crystal method: uses a single
crystal with rotating angle, and a monochromatic
X-ray
• The Debye-sherrer method: uses a polycrystalline
or powered sample, and a monochromatic X-ray
1.4 The periodic table
The periodic system of the elements
—— An ordering of the elements according to periodically
recurring chemical and physical properties.
• The periodically repeated chemical properties:
the monovalence of the alkali atoms:
3Li, 11Na, 19K, 37Rb, 55Cs, 87Fr
and the lack of reactivity of the rare gases:
2He, 10Ne, 18Ar, 36Kr, 54Xe, 86Rn
• The periodically repeated physical properties: the
atomic volumes and the ionisation energies
The periodic system of the elements
Atomic volumes and ionisation energies as function of the position in the
periodic system of the elements. Particularly noticeable are the (relatively)
large atomic volumes of the alkali metal atoms and the large ionisation
energies of the noble gas atoms.
The empirical regularities indicate corresponding
regularities in the atomic structure –– table of
periodic system of the element.
The periodic table of the elements was first
proposed in 1869 by Medeleev and Lothar Meyer.
It is constructed by listing the atoms (elements)
according to increasing the nuclear charge number
Z.
1.5 Isotope
The relative atomic masses Arel (by chemical method):
near integer
Mass number A: the hypothesis of Prout (in 1815), all
atoms are made up of H atoms.
A and Arel are nearly equal at many cases, but for
Chlorine (17Cl), Arel = 35.5, for 38Sr, Arel = 87.62
With the aid of mass spectroscopy, Aston in 1920, the
composition of naturally occuring Neon (10Ne) with
the mass number A = 20, 21 and 22
Isotopes: atoms with the same nuclear charge number
Z and differing mass numbers A
Many elements consist of several isotopes
Isotopes
abundance
the relative atomic mass Arel
20
90.92%
19.99244
10 Ne
21
0.26%
20.99385
10 Ne
22
8.82%
21.99138
10 Ne
average Arel = 20.18
35
75.4%
17 Cl
37
24.6%
17 Cl
average Arel = 35.457
1
99.986%
1H
2
0.014%
1H
3
(Deuterium, not natural)
1H
average Arel = 1.008
Elements with only one stable isotope:
9
4
Be
27
13
Al
127
53
I
Isotope separation —— a problem of
technology and nuclear physics
Separation of isotopes of
1
2
H
1
and 1 H , relatively easy,
238
235
and
is more difficult.
U
92 U
92
Methods of isotope separation (from economics and
the state of technology)
a) Electromagnetic separation : expensive and slow
1mg per hour at a current of 10-4 A,
to separate 35g Cl, it needs 30 years
b) By means of diffusion in a gas:
2
2
v1 / v2  m2 / m1 , since m1v1  m2 v2
c) The gas centrifuge:
heavier isotope is acted upon by a stronger
centrifugal force
d) Thermodiffusion in a separation tube:
temperature gradient in a mixture of gases
e) Fractional distillation:
heavier isotope in general has the higher
boiling point
f) Electrolysis
molecules with heavier isotope are less easily
decomposed than those with the lighter isotope
g) Chemical reactions
molecules with differing isotopic compositions
react with different rates.
h) Laser photochemistry
for certain isotopes using photochemical
reactions.
Homework:
Pp36, problems 3.2, 3.3