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 m

ultiples 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 12CTo be expedient for the experimental precision determination of atomic masses b

y 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:

kgN

molgCm

A

27126 1092516.19

/12)(

kgOm 27105584.26)(

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

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:

222

2x

e

m

Bl

Ey

oven

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 1918c) Double focussing – velocity and directional fo

cussingd) 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

Bragg (in 1913) interference condition:1= 2 =

With the X-ray path difference: = AB+BC-AE = n

Incident X-rays

Incident X-rays

Diffracted x-rays

Diffracted x-rays

Atomic planes

1 2

1 2

2dsin = n

atoms

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

• 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

—— An ordering of the elements according to periodically recurring chemical and physical properties.

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

90.92% 19.992440.26% 20.993858.82% 21.99138average Arel = 20.1875.4%24.6%average Arel = 35.45799.986%0.014%

(Deuterium, not natural)average Arel = 1.008

Elements with only one stable isotope:

Ne2010

Ne2110

Ne2210

Cl3517

Cl3717

H11

H21

H31

Be94

Al2713 I127

53

Isotope separation —— a problem of technology and nuclear physics

Separation of isotopes of

and , relatively easy,

and is more difficult.

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

H11 H2

1

U23592 U238

92

b) By means of diffusion in a gas: , since

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 bo

iling point

1221 // mmvv 222

211 vmvm

f) Electrolysis molecules with heavier isotope are less easily

decomposed than those with the lighter isotope

g) Chemical reactionsmolecules with differing isotopic compositions react with different rates.

h) Laser photochemistryfor certain isotopes using photochemical reactions.

Homework:

Pp36, problems 3.2, 3.3