atoms & nuclei notes.docx

8/14/2019 Atoms & nuclei notes.docx

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The Structure of an Atom:

Introduction:

The first model of an atom was proposed by J. J. Thomson in 1898. According to

this model, an atom consists of positively charged matter in which the negatively

charged electrons are uniformly embedded like plums in a pudding. This model was

picturesquely calledplum pudding model of the atom.

However, this model had several drawbacks, that

could not accurately describe observed emission or

absorption spectra of an atom, and more significantly,

scattering of charged particles from atoms.

Alpha-particle scattering and Rutherfords nuclear model of atom:

Ernst Rutherford, a former research student of J.J.Thomson, proposed a classic

experiment of scattering of -particles by atoms, emitted by some radioactive elements

to investigate the atomic structure proposed by J.J. Thomson (plum pudding model).

Rutherford Atomic Model known as

The Scientists Hans Geiger and Ernest Marsden carried out a series of -

particle experiments to probe the structure of atoms under the direction of Ernest

Rutherford, known as the GeigerMarsden experiment (also called the Rutherford

gold foil experiment). The experiments conducted, gave some unexpected results &

demonstrated for the first time the existence of theatomic nucleus, leading to the

downfall of theplum pudding modelof the atom, and the development of theRutherford

(or planetary) model.

Construction of the experiment:

It has a radioactive source rich in positively charged heavy alpha particles inside a cube

shaped thick lead box with a narrow opening.
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The alpha particles were confined

to a narrow beam by passing them

through a lead sheet through a slit.

An extremely thin gold foil was

bombarded with the narrow beam

of fast moving alpha particles. On

bombarding the alpha particles

were scattered in different

directions with different angles and

were detected by florescent

rotatable detector which has a

microscope and a screen coated with zinc sulphide. The whole experimental setup was

placed in an evacuated chamber to prevent scattering by the air molecules. These

particles after striking on the screen caused scintillations. Before performing this

experiment it was assumed by Rutherford that most of the alpha particles would pass

through the gold foil with less deflection. He assumed this on the basis of theory

proposed by JJ Thomson. This was assumed because the alpha particles are heavy

and the negative charge in the "plum pudding model" is widely spread.


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After performing his experiment he made observations:

Almost all the alpha particles did pass through the foil but

Some alpha particles were deflected off at different angles as observed at the

screen of the detector.

Very few of the alpha particles (one or two) even bounced backwards after hitting

the gold foil.

On the basis of these observations Rutherford made the following conclusions

regarding the model of an atom:

1. Since most of the alpha particles passed straight through the gold foil without any

deflection, most of the space within the atoms is empty.

2. Since some of the alpha particles (which are big in size) were deflected by large

angles or bounced backwards, they must have approached such region which is

located at the center of the atom where greater part of its mass and positive

charge were tightly concentrated; otherwise it would not able to impart large

repulsive force to bounce back some of the alpha particles. This positively

charged region is called the nucleus of the Atom.

3. As very few alpha particles undergone the deflection it was concluded that the

volume occupied by the central region (nucleus) is very small.

4. The atom is surrounded by a suitable number of electrons so that their total

negative charge is equal to the total positive charge of the nucleus and the atom

as a whole is electrically neutral.

5. The electrons revolve around the nucleus in various orbits just as planets revolve

around the sun. The centripetal force required for their revolution is provided by

the electrostatic attraction between the electrons and the nucleus.

There were mainly two defects in Rutherford's atomic theory as follows:


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1. According to classical electromagnetic theory, being a charged particle, electron

must emit energy when it is accelerated. We know that around the nucleus, the

motion of electron is an accelerated motion, hence it must radiate energy. But

this does not happen in actual practice. Assume that if it occurs then due to

continuous loss of energy orbit of electron must decrease continuously. As a

result electron will fall into the nucleus eventually after some time. But this is

against the practical situation and hence this shows that atom is unstable.

2. If the electrons emit energy continuously, continuous spectrum should be formed.

But in practical line spectrum is observed.

Electrostatic force of repulsion between the alpha-particle and the positivelycharged nucleus:

Alpha particles are nuclei of helium atoms and, therefore, carry two units, 2e, of

positive charge and have the mass of the helium atom. The charge of the gold nucleus

is Z.e, where Z is the atomic number of the atom; for gold Z = 79. Since the nucleus of

gold is about 50 times heavier than a -particle, it is reasonable to assume that it

remains stationary throughout the scattering process.

Electrostatic force of repulsion between the alpha-particle and the positively charged

nucleus is obtained by employing Coulombs law. Magnitude of the force is

where r is the distance between the -particle and the nucleus. The force is directed

along the line joining the -particle and the nucleus.

Distance of Closet approach (d):

Suppose an -particle of mass m scattered from a radio-active source moves with a

velocity v directly towards the nucleus of an atom of atomic number Z. On approaching

maximum possible nearest position to nucleus, it experiences large repulsive force, its

motion momentarily stops & then either deflects away or bounce backwards from the

nucleus. The maximum possible nearest position of Alpha-particle from the nucleus at

which its motion momentarily stops is called the Distance of Closet approach (d).


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The Alpha-particle initially moves with a kinetic energy K (1/2mv2) & it gets completely

converted into its potential energy U at stopping point, as per the conservation of

energy. Therefore,

or,

In Geiger-Marsden Experiment, kinetic energyK (1/2mv2) =5.5 MeV & atomic no. of

Gold 79. 1/40= 9.0 109 N m

2

/C

2

& e = 1.6 1019 C, we have, after substitutingin the above equation, d= 41.3 fm. [1 fm (i.e. fermi) = 1015 m.]

Impact Parameter (b): The perpendicular distance of the velocity vector of the -

particle from the centre of the nucleus when it is far away from the nucleus is known as

impact parameter. The shape of the trajectory of the scattered -particle depends on the

impact parameter b and the nature of the potential field. Rutherford deduced the

following relationship between the impact parameter b and the scattering angle :


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Atomic Structure: The Bohr Model of Hydrogen Atom

In order to overcome the difficulty associated with the collapse of the electron into the

nucleus as per the classical electromagnetic theory, Niels Bohr made certain

modifications in the Rutherfords Atomic Model by adding the ideas of the newly

developing quantum hypothesis. Bohr combined classical and early quantum concepts

and gave his theory in the form of three postulates.

These are:

(i) An electron in an atom could revolve in certain stable orbits, called

stationary orbits in which it doesnt emit Electromagnetic Radiation.

According to this postulate, each atom has certain definite stable

states, in which itcan exist, and each possible state has definite total

energy. These arecalled the stationary states of the atom.

(ii) In stationary states of an atom, electron revolves around the nucleus in

those stationary orbits, for which the angular momentum is some

integral multiple of h/2 where h is the Plancks constant. Thus the

angular momentum (L) of the orbiting electron is quantised i.e., is L =

nh/2, where n=1, 2, 3 etc., but never non-integer values.

(iii) An electron might make a transition from one of its specified non-

radiating orbits to another of lower energy. When it does so, a photon

is emitted having energy equal to the energy difference between the

initial and final states. The frequency of the emitted photon is then

given by h = EiEf, where Eiand Efare the energies of the initial and

final states and Ei> Ef.

For Hydrogen Atom:

Consider the electron of hydrogen atom, with mass m and charge - e moves in a circular

orbit of radius rn with constant tangential velocity vn in an nth. possible orbit. The

attractive Coulomb force (Fe) provides the requisite centripetal force (Fc) to maintain

orbital motion (neglecting the motion of the nucleus since its mass is much greater than

the electron) Thus, for a dynamically stable orbit in a hydrogen atom,


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Substituting the values of orbital radius rn, we have

Substituting the values of constant we get,

Atomic energies are often expressed in electron volts (eV) rather than joules. Since

1 eV = 1.6 1019 J, above eq. can be rewritten as

The negative sign of the total energy of an electron moving in an orbit means that the

electron is bound with the nucleus. Energy will thus be required to remove the electron

from the hydrogen atom to a distance infinitely far away from its nucleus (or proton in

hydrogen atom).

Energy L evel Diagram. It is a diagram in which the energies of the different stationary

states of an atom are represented by parallel horizontal lines, drawn according to some

suitable energy scale.

According to Neils Bhor, an electron revolves around the nucleus in certain

stable stationary orbit with definite total energy & without radiating energy. It can make

transition from one stationary orbit of certain energy level to a other of different energy.

Thus the electrons in atoms are in orbits of differing energy around the nucleus (think of


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planets orbiting around the sun). The term energy level (or Shell) is used to describe

these orbits of different energy.

The energy level an electron normally occupies is called its ground state and is

the lowest energy state with orbit of smallest radius . But it can move to a higher-

energy, less-stable level, or shell, by absorbing energy. This higher-energy, less-

stable state is called the electrons excited state. For moving an electron to a

higher energy level from the ground state, certain minimum energy is required,

called the ionization energy, which is nothing but the energy of the electron at

ground state. Excitation energy at a particular excite state is the energy

difference between the initial & final state of excitation.

After an electron is being excited, it can return to its original ground state by

releasing the energy it has absorbed, as shown in the diagram below.

Bohr found that the closer an electron is to the nucleus, the less energy it needs,

but the farther away it is, the more energy it needs. So Bohr numbered the

electrons energy levels. The higher the energy-level number, the farther away

the electron is from the nucleus and the higher the energy.

Below is the energy diagram for an Hydrogen Atom. The energy at a particular

level is found by using the total Energy formula for hydrogen atom which is

Where n=1,2, 3,etc. defines theenergy level.


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The spectrum of hydrogen Atom:

Each element gives a characteristic line spectrum, the lines arising from electron

transitions within the atom. With one electron and one proton, hydrogen is the simplest

element and gives the simplest line spectrum.

The spacing between lines within certain sets of the hydrogen spectrum

decreases in a regular way. Each of these sets is called a spectral series. The first such

series was observed by a Swedish school teacher Johann Jacob Balmer in the visible

region of the hydrogen spectrum. This series is called Balmerseries. Balmer found a

simple empirical formula for the observed wavelengths

where is the wavelength, R is a constant called the Rydberg constant, and n may

have integral values 3, 4, 5, etc. The value of R is 1.097 107 m1. This equation is

also called Balmer formula.

In general, the above formula is written as,

[ ]where nf = 2 & ni = 3,4,5,..etc. (for Balmer Series)

Balmer found that with the decrease of wavelength the spacing between spectral lines

decreases. Lines appear closer together and are weaker in intensity.

In Balmer Series, the electron transitions involves to second energy level (n=2) from

higher energy levels (n=3,4,5..etc.).

There are other spectral series, which were identified in due course, through

spectroscopic investigations & are named after their discovered. Different spectral lines

are listed below:


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1. Lyman Series. Here ni = 2, 3, 4,..and nf = 1. This series lies in the

ultraviolet region.

2. Balmer Series. Here ni = 3, 4, 5,. and nf = 2. This series lies in the visible

region.

3. Paschen Series. Here ni= 4, 5, 6,.. and nf = 3. This series lies in the

infrared region.

4. Brackett Series. Here ni = 5, 6, 7,.. and nf = 4. This series lies in the

infrared region.

5. Pfund Series. Here ni = 6, 7, 8,. and nf = 5. This series lies in the infrared

region.

Line spectra originate in transitions between energy levels.


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It does not include the electrical forces between electrons which

necessarily appear in multi-electron atoms.

2. While the Bohrs model correctly predicts the frequencies of the light

emitted by hydrogenic atoms, the model is unable to explain the relative

intensities of the frequencies in the spectrum. In emission spectrum of

hydrogen, some of the visible frequencies have weak intensity, others

strong. Why? Experimental observations depict that some transitions are

more favoured than others. Bohrs model is unable to account for the

intensity variations.

In short, efficiencies of the Bohr model are describe as

Cannot be applied to multi-electron atoms.

Does not predict the fine structure of atomic spectral lines.

Does not provide a method to calculate relative intensities of

spectral lines.


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NUCLEI

Composition of Nucleus:

Nucleus was discovered by Rutherford. It is the core of an atom where almost all the masses of the atom & positive

charge is concentrated. Its volume is very less compare to the volume of atom

(volume of a nucleus is about 1012

times the volume of the atom).

Nucleus consists of Protons & Neutrons except Hydrogen which has only one

proton.

Proton is a fundamental particle with positive charge 1.6 x 10-19C and mass 1.67

x 10-27kg (1836 times heavier than an electron).

Neutron is also a fundamental particle with no charge and mass 1.675 x 10-27

kg

(1840 times heavier than an electron).

The composition of a nucleus can be described using the following terms and symbols:

Z - atomic number = number of protons

N - neutron number = number of neutrons

A Atomicmass number = Z + N = total number of protons and neutrons

One also uses the term nuc leon for a proton or a neutron. Thus the number of

nucleons in an atom is its mass number A.

Atom ic Number(Z) is the number of protons in a nucleus of an atom.

Atomic Mass n umber(A) is the total nos. of protons & neutrons in the nucleus of an

atom. Sometimes referred as nucleon.

Nuclear species or nuclides are shown by the notation , where x is the chemicalsymbol of the atom.{ }


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For example, the nucleus of gold is denoted by . It contains 197 nucleons, ofwhich 79 are protonsand the rest 118 are neutrons.

Atomic Mass Unit (amu): It is use to express the mass of an atom & is defined

as is (1 /12)th. of mass of 1 atom of carbon.

1amu =

x (mass of one 12C atom)=

x

g = 1.66 x 10-27Kg.

Size of Nucleus:

Nucleus does not have a sharp or well-defined boundary. A nucleus can be

considered to be spherical in shape and assigned a radius. Electron scattering

experiments allow determination of the nuclear radius; it is found that radii of

nuclei fit the formula

R = R0A1/3,

whereR0= 1.2 x 10-15m =1.2 fmis a constant and A is the mass number of the

nucleus.

Nuclear Volume, V = (4/3)R3= (4/3)R0

3A (V A )

Nucleus Density:

Mass of nucleus, M = A amu = A x 1.66 x 10-27kg

Nuclear Volume, V = (4/3)R3= (4/3)R0

3A

= (4/3) x (22/7) x (1.2 x 10-15

)3A m

3

= 7.24 x 10-45A m3

Therefore, Nucleus Density, = M / V = 2.29 x 1017kg / m3

The density of nucleus is a constant, independent of Atomic mass no. (A). So, allthe nuclei possess nearly the same density. This density is very large compared

to ordinary matter, say water, which is 103 kg m3. This is because most of the

space in an atom is empty & almost all the masses of an atom is concentrate in a

small volume of nucleus.


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Isotopes:Isotopes are the atoms of the same elements which possess identical

chemical properties & but has different mass. In other words they are atoms

having same Atomic no. (Z) but different Atomic mass no. (A).

Deuterium,

, which is an isotope of hydrogen, contains one proton and

one neutron. Its other isotope tritium, , contains one proton and twoneutrons. The element gold has 32 isotopes, ranging from A =173 to A =

204.

(The chemical properties of an atom are determined by its atomic number

i.e., no of protons. Hence isotopes of an element has similar chemical

properties due to same atomic no. but different atomic mass due to

unequal neutrons.)

Isobars: Nuclei with same mass number A but different atomic no. are called

isobars. For example, the nuclides and are isobars. Isotones:Nuclei with same neutron number N but different atomic number Z, are

called isotones. For example and are called isotones.

atoms & nuclei notes.docx

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