Plate forme d'enseignement à distance

Chapter I :structure of matter

 

I.1. MATTER (WHAT IS MATTER?):

Matter consists of everything that has mass and occupies a volume in space.

Matter can exist in three different physical states:

 Solid state: has a defined volume and shape.

 Liquid state: has a defined volume but no precise shape, it takes the shape of its container

 Gaseous state: has neither a defined volume nor a defined shape, it takes the volume and shape of its container.

I.1.1.Fundamental units of measurement of matter:

Longueur: Length

Courant électrique: electric current

·        Notion of atom, molecules, mole and Avogadro's number

·        Atoms combine to form molecules, a molecule is therefore a union of atoms.

·        The mole is the unit of measurement of the quantity of matter.

·        The number of atoms contained in a mole is called the Avogadro's Number (NA) NA = 6.023 1023

1mole (of atoms, ions, molecules….) = 6.023 1023 (atoms, ions, molecules….).

I.1.2. THE NUMBER OF MOLES AND THE MOLAR VOLUME

The number of moles designates the quantity of matter: the molar mass is the Definition: The number of moles is the ratio between the mass of the compound and its molar mass

n: number of moles

m: mass of compound in g

M: molar mass of compound in g/mol

Case of gaseous compounds: Avogadro-Ampère law

·        always occupies the same volume. This volume is the molar volume (MV):

M = 22.4 l/mol in this case m = V/22.4

 

I.1.3ATOMIC MASS UNIT (a.m.u)

The masses of particles (e, p, n…) are not at all on our scale, so we use a mass unit different from Kg but better adapted to the measured quantities, it is the a.m.u or (u)

1 a.m.u = 1/12 mC = 1/NA = 1.66.10-24 g = 1.66. 10-27 Kg (mc = 12/N)

I.1.4. ATOMIC MOLAR MASS AND MOLECULAR MOLAR MASS

The atomic molar mass: is the mass of one mole of atoms.

Ex: MC= 12.0 g.mol-1 and M0 = 16.0 g.mol-1

 The molecular molar mass: is the mass of one mole of molecules.

Ex: The molar mass of water H2O: MH2O= 2.1+16=18 g.mol-1

 

I.2. CONCENTRATIONS:

Concentrations are quantities with units used to determine the proportion

of solutes in relation to that of the solvent. Depending on the nature of the unit chosen, we distinguish:

1) Molarity (CM): expresses the number of moles of solute per liter of solution.

2) Molality (Cm): expresses the quantity of solute contained in 1000g of solvent.

3) Normality (N): expresses the number of gram equivalents of solute per liter of solution (eq.g/l).

 The gram equivalent is the quantity of substance comprising one mole of the particles considered (H+, OH–, e–, etc.)

4) The percentage % of a solution indicates the mass of substance per 100g of solution. This is a weight-to-weight comparison

5) Mole fraction (xi): indicates the ratio between the number of moles and the total number of moles in the solution.

I.2.1. DILUTION OF AN AQUEOUS SOLUTION:

solvent (water). The initial solution of higher concentration is called the mother solution.

The final solution of lower concentration is called the daughter solution (diluted solution). During dilution, the quantity of solute matter is conserved so that we can write:

ni = nf ⇒ CiVi = CfVf

With n: quantity of matter; V: volume and C: concentration

i: initial, i.e. relative to the mother solution.

f: final, i.e. relative to the diluted solution.

 

I.3. Principal constituents of the atom:

The atom is essentially made up of three elementary particles. It is an electrically neutral entity. It contains a given number of protons and neutrons also called nucleons (constituents of the nucleus), surrounded by electrons.

Electrical neutrality is due to the equality of the number of nuclear charges (protons) and electrons. This number, called the atomic number, is designated by Z.

Example: Constituent of some element.

I.4. Isotopy and relative abundance of different isotopes:

- The atoms of a natural element can differ in the number of neutrons. We then say that the element has isotopes.

Isotopes are atoms of the same element whose nuclei have the same number

of protons and a different number of neutrons.

Examples: Natural hydrogen is made up of three isotopes.

 

All chemical elements are symbolized by:

- If the element has several isotopes, its experimental mass is a weighted average of the atomic mass of the different isotopes.

-Mi and ai = atomic mass and relative abundance of isotope i

Example 1: Chlorine is made up of two isotopes

Example 2:

⁴₂ He contains 4 nucleons: 2 protons and 4 – 2 = 2 neutrons.

₉₂²³⁸ U contains 92 protons and 238 – 92 = 146 neutrons.

I.4.1. Quantity of matter

It characterizes the quantity of matter contained in a body. SI unit: the mole (mol)

I.4.2.Avogadro's number NA (Avogadro's constant)

Avogadro's number NA is the number of entities contained in a quantity of

matter of 1 mole, therefore: (donc)

 

The elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles or specified groupings of such particles.

I.4.3. Molar mass M/

It constitutes the mass of one mole of atoms or molecules, therefore 6.02×10²³ atoms or molecules.

From the molar mass we can calculate the mass of an atom, m0:

I.5- Conservation laws/

a) Mass defect (défaut de masse):

In nuclear reactions, mass is not conserved. The mass defect is the difference between the mass of the initial particles and that of the final particles.

b) Binding energy: (Enérgie de cohésion)

Atomic nuclei owe their cohesion to the strong interaction force between nucleons. This is a short-range attractive force. It is far more important than repulsive electrical forces.

Mass defect: We note that the sum of the masses of the A nucleons composing an atomic nucleus is always greater than the mass of the nucleus ^A _ZX:

To disperse all the nucleons in the nucleus, it is therefore necessary to provide the nucleus with the energy Δm×c2. This energy represents the binding energy EL of the nucleus:

E_L is also the energy that is released if we build an atomic nucleus from its components.

I.6. Radioactivity - Nuclear reactions:

I.6.1. Stability of nuclei and determination of the cohesion energy per nucleon:

The stability of a nucleus is all the higher as the binding energy per nucleon is high, it is close to 8Mev/nucleon for most stable nuclei.

Therefore:          7.5< E_L<8.8 Mev

 

I.7. Radioactivity nuclear reactions:

Radioactivity is the name given to the transformation of atomic nuclei during which radiation is emitted.

These radiations are, for example,

Rayon= radius

 

 

Natural radioactivity is that which exists naturally in nature.

Artificial radioactivity is that obtained by bombardment of atomic nuclei by particles (neutrons, protons, α particles, electrons, positrons, etc.). We found:

-Transmutation reaction:

These reactions produce nuclides with a mass number equal to or very close to that of the nuclide which served as the target. (Ces réactions produisent des nucléides de nombre de masse égal ou trés proche de celui du nucléide qui a servi de cible).

-Fission reaction:

A heavy nucleus decays to form at least two lighter nuclei of comparable masses with the emission of neutrons (Un noyau lourd se disintégre pour donner au moins deux noyaux plus légers de masses comparables avec émission de neutrons).

-Fusion reaction:

It is the union of two or more light nuclei into a heavier nucleus under high temperature. (C'est la réunion de deux ou plusieurs noyaux légers en un noyau plus lours sous haute température).

a)    Alpha decay: (Disintegration α):

Some heavy nuclei (N+Z > 200) emit alpha particles (or helium nuclei). Balanced equation (Certains noyaux lourds (N+Z > 200) émettent des particules alpha (ou noyaux d’hélium). Equation bilan) ::

 

Example :

b) β- disintegration :

 

Nuclei with excess neutrons (Les noyaux avec un surplus de neutrons), emit an electron which comes from the decomposition of a neutron into a proton.

 

Sr= Srontium

 

b)    β+ decay:

 

Nuclei with too many protons  emit a positron which comes from the

decomposition of a proton into a positron, a neutron.

 

 

 

c)     γ decay:

 

 

After a radioactive transformation of the nucleus, the daughter nucleus is in an excited state (*) and de-excites by emitting one (or mor e) high-energy photons (gamma) (Après une transformation radioactive du noyau, le noyau fils est dans un état excité (*) et se

désexcite en émettant un (ou plusieurs) photons de haute énergie (gamma)).

 

I.7.1. Radioactive Decay Law:

 

The aim is to determine the statistical evolution of the number N of radioactive nuclides present in a specimen. This involves establishing the mathematical equation for the decrease in N as a function of time t.

Initial condition: at time t = 0, the sample contains N0 radioactive nuclei.

At time t, there are N. At time t+dt there are only N+dN < N (dN < 0).

dN is the number of nuclei that disintegrate in the time interval dt.

(Le but est de déterminer l'évolution statistique du nombre N de nucléides radioactifs présents dans un échantillon. Il s’agit d’établir l’équation mathématique de la diminution de N en fonction du temps t.

Condition initiale : à l’instant t = 0, l’échantillon comprend N0 noyaux radioactifs.

A l’instant t, il y en a N. A l’instant t+dt il n’y en a plus que N+dN < N (dN < 0).

dN est le nombre de noyaux qui se désintègrent dans l’intervalle de temps dt).

 

λ > 0 is the decay constant; unit: s-1 (la constant de disintegration).

We therefore have the following differential equation:

To solve this differential equation we look for the primitive to the left and right of the equality sign.

 

I.7.2. Half-life T of a radioelement: (Demi-vie T d'un radioélément)

 

The half-life T of a radioelement is the time at the end of which the number N has decreased by half. The half-life of radioactive nuclei can extend from fractions of a second to billions of years. It is characteristic of a particular nuclide (On appelle demi-vie T d’un radioélément le temps au bout duquel le nombre N a diminué de moitié. La demi-vie des noyaux radioactifs peut s’étendre de fractions de secondes jusqu’à des milliards d’années. Elle est caractéristique d’un nucléide particulier.

 

I.7.3. Relationship between T and λ:

I.7.4. Activity of a radioactive source/

 

The activity A of a radioactive source is the number of radioactive nuclei that disintegrate per second. It is also the number of particles or photons emitted per unit of time. If in a time interval dt, dN atoms have disintegrated, the activity is: (L’activité A d’une source radioactive est le nombre de noyaux radioactifs qui se désintègrent par seconde. C'est aussi le nombre de particules ou de photons émis par unité de temps. Si dans un intervalle de temps dt, dN atomes se sont désintégrés, l’activité vaut) :

Applications

 Dating in archaeology: The isotope C-14 is β- radioactive with a half-life of 5730 years. 14 C is created in the atmosphere by cosmic ray bombardment. It is then absorbed by plants in the form of carbon dioxide. When the plants die, absorption ceases and the carbon C-14 disintegrates over time. The activity provides information on the date of the organism's death.

 

Example: In a carbon sample taken from a mummy, the activity of C-14 has decreased to 60% of the initial value. Calculate the date of death of the person.