PHY 004: MODERN PHYSICS

LECTURE I

Drs. A. O. AKALA, K. OGUNGBEMI, & N. E. ERUSIAFE

Atomic Structure All matter is composed of atoms.

Understanding the structure of atoms is critical to understanding the properties of matter

Evolution of Atomic Theory

Dalton’s Model

In the early 1800s, theEnglish Chemist John Dalton performed a number of experiments that eventually led to the acceptance of the idea of atoms.

HISTORY OF THE ATOM

1808 John Dalton

suggested that all matter was made

up of tiny spheres that were able

to bounce around with perfect

elasticity and called them

ATOMS

8 X2Y16 X 8 Y+

DALTONS ATOMIC THEORY

Dalton’s Theory

• He deduced that all elements are composed of atoms. Atoms are indivisible and indestructible particles.

• Atoms of the same element are exactly alike.

• Atoms of different elements are different.

• Compounds are formed by the joining of atoms of two or more elements.

Thomson’s Plum Pudding Model

• In 1897, the English scientist J.J. Thomson provided the first hint that an atom is made of even smaller particles.

Thomson’s Model• He proposed a model

of the atom that is sometimes called the “Plum Pudding” model.

• Atoms were made from a positively charged substance with negatively charged electrons scattered about, like raisins in a pudding.

Thomson’s Model

• Thomson studied the passage of an electric current through a gas.

• As the current passed through the gas, it gave off rays of negatively charged particles.

Thomson’s Model• This surprised Thomson, because the

atoms of the gas were uncharged. Where had the negative charges come from?

• Thomson concluded that the negative charges came from within the atom.

• A particle smaller than an atom had to exist.

• The atom was divisible!

Thomson called the negatively charged “corpuscles,” today known as electrons.

Since the gas was known to be neutral, having no charge, he reasoned that there must be positively charged particles in the atom.

But he could never find them.

Thomson’s Model

HISTORY OF THE ATOM

1898 Joseph John Thompson

found that atoms could sometimes

eject a far smaller negative

particle which he called an

ELECTRON

J.J. Thomson, measured mass/charge of e-

(1906 Nobel Prize in Physics)

A = alphaB = gammaC = beta

Limitation of the Thompson’s Model

It could not explain the scattering experiment performed by Rutherford.

gold foil

helium nuclei

Charge of an electron

Millikan oil drop experiment

Millikan’s Oil Drop Experiment

I. Charge of electron – very important application of uniform electric field between two plate – Robert Millikan (1868-1953)

A. Purpose: to find charge of an electron

1. Fine oil sprayed into air in top – gravity causes them to fall

2. A few enter the hole

3. Potential difference between plates is applied – exerts a force on the charged drops

4. Top plate is positive enough that negative drops will rise

-

5. Potential difference adjusted to suspend (float) particle

-E*q = m*g

6. Electric field was determined from potential difference between two plates (E = V/d)

-

7. Found velocity of charge when field was turned off. Using velocity, mg was found. Using E & mg, the charge could be calculated.

-

8. The drops had a variety of charges. So, he ionized the air, added or removed electrons. The change in charge was always a multiple of -1.6 x 10-19 C. Thus, the charge on one electron.

-

9. Showed that charge is quantized – an object can only have charge with a magnitude that is some integral of the charge of an electron.

-

HISTORY OF THE ATOM

1910 Ernest Rutherford

oversaw Geiger and Marsden carrying

out his famous experiment.

they fired Helium nuclei at a piece

of gold foil which was only a few

atoms thick.

they found that although most of

them passed through. About 1 in

10,000 hit

Rutherford’s Gold Foil Experiment

• In 1908, the English physicist Ernest Rutherford was hard at work on an experiment that seemed to have little to do with unraveling the mysteries of the atomic structure.

– Most of the positively charged “bullets” passed right through the gold atoms in the sheet of gold foil without changing course at all.

– Some of the positively charged “bullets,” however, did bounce away from the gold sheet as if they had hit something solid. He knew that positive charges repel positive charges.

Rutherford’s Gold Foil Experiment

Rutherford’s experiment.

Rutherford’s Gold Foil Experiment

• This could only mean that the gold atoms in the sheet were mostly open space. Atoms were not a pudding filled with a positively charged material.

• Rutherford concluded that an atom had a small, dense, positively charged center that repelled his positively charged “bullets.”

• He called the center of the atom the “nucleus”• The nucleus is tiny compared to the atom as a whole.

Rutherford’s Gold Foil Experiment

Rutherford’s Model

Rutherford reasoned that all of an atom’s positively charged particles were contained in the nucleus. The negatively charged particles were scattered outside the nucleus around the atom’s edge.

Limitations of the Rutherford’s Model

According to Rutherford’s model of an atom, electrons revolve around the nucleus as planets revolve around the sun. But, electrons revolving in circular orbits will not be stable because during revolution, they experience acceleration. Due to acceleration, they will lose energy in the form of radiation arid fall into the nucleus. In such a cases the atom would be highly unstable and would collapse.

Bohr ModelIn 1913, the Danish scientist Niels Bohr proposed an improvement. In his model, he placed each electron in a specific energy level.

Bohr ModelAccording to Bohr’s atomic model, electrons move in definite orbits around the nucleus, much like planets orbit around the sun. These orbits, or energy levels, are located at certain distances from the nucleus.

HISTORY OF THE ATOM

1913 Niels Bohr

studied under Rutherford at the

Victoria University in

Manchester.

Bohr refined Rutherford's idea

by adding that the electrons

were in orbits. Rather like

planets orbiting the sun. With

each orbit only able to contain

a set number of electrons.

1. e- can have only specific (quantized) energy values

2. light is emitted as e- moves from one energy level to a lower energy level

Bohr’s Model of the Atom (1913)

En = -RH ( )1n2

n (principal quantum number) = 1,2,3,…

RH (Rydberg constant) = 2.18 x 10-18J

The Bohr Model of the Atom

The Bohr Model of the Atom:Ground and Excited States

• In the Bohr model of hydrogen, the lowest amount of energy hydrogen’s one electron can have corresponds to being in the n = 1 orbit. We call this its ground state.

• When the atom gains energy, the electron leaps to a higher energy orbit. We call this an excited state.

• The atom is less stable in an excited state and so it will release the extra energy to return to the ground state.– Either all at once or in several steps.

Line Emission Spectrum of Hydrogen Atoms

Every element has a unique emission spectrum

The Bohr Model of the Atom:Hydrogen Spectrum

• Every hydrogen atom has identical orbits, so every hydrogen atom can undergo the same energy transitions.

• However, since the distances between the orbits in an atom are not all the same, no two leaps in an atom will have the same energy.– The closer the orbits are in energy, the lower the energy of the photon emitted.

– Lower energy photon = longer wavelength.

• Therefore, we get an emission spectrum that has a lot of lines that are unique to hydrogen.

The Bohr Model of the Atom:Hydrogen Spectrum

Ephoton = DE = Ef - Ei

Ef = -RH ( )1n2f

Ei = -RH ( )1n2i

i fDE = RH ( )1

n2

1n2

RH is the Rydberg constant

n is the principal quantum number

En = -RH ( )1n2

Bohr showed the energy a H atom can have is equal to:

Light emission of sodium atom

Line spectrum

It is in violation of the Heisenberg Uncertainty Principle. The Bohr Model considers electrons to have both a known radius and orbit, which is impossible according to Heisenberg.

The Bohr Model is very limited in terms of size. Poor spectral predictions are obtained when larger atoms are in question.

It cannot predict the relative intensities of spectral lines.

It does not explain the Zeeman Effect, when the spectral line is split into several components in the presence of a magnetic field. The Bohr Model does not account for the fact that accelerating electrons do not emit electromagnetic radiation.

Limitations of Bohr’s Model

Electron Cloud• A space in which electrons are likely to be found.

• Electrons whirl about the nucleus billions of times in one second

• They are not moving around in random patterns.

• Location of electrons depends upon how much energy the electron has.

Electron Cloud

• Depending on their energy they are locked into a certain area in the cloud.

• Electrons with the lowest energy are found in the energy level closest to the nucleus

• Electrons with the highest energy are found in the outermost energy levels, farther from the nucleus.

Atomic Structure

Atoms are composed of-protons – positively charged particles-neutrons – neutral particles-electrons – negatively charged particles

Protons and neutrons are located in the nucleus. Electrons are found in orbitals surrounding the nucleus.

HELIUM ATOM

+N

N

+-

-

proton

electronneutron

Shell

Atomic StructureEvery different atom has a characteristic number of protons in the nucleus.

atomic number = number of protons

Atoms with the same atomic number have the same chemical properties and belong to the same element.

ATOMIC STRUCTURE

the number of protons in an atom

the number of protons and neutrons in an atom

He

2

4Atomic mass

Atomic number

number of electrons = number of protons

ATOMIC NUMBER (Z) = number of protons in nucleus

MASS NUMBER (A) = number of protons + number of neutrons

= atomic number (Z) + number of neutrons

ISOTOPS are atoms of the same element (X) with different numbers of neutrons in the nucleus

XA

Z

H11 H (D)

21 H (T)

31

U23592 U

23892

Mass Number

Atomic NumberElement Symbol

Atomic Structure

Atomic Structure

The Wave Model

Today’s atomic model is based on the principles of wave mechanics.

According to the theory of wave mechanics, electrons do not move about an atom in a definite path, like the planets around the sun.

The Wave Model

In fact, it is impossible to determine the exact location of an electron. The probable location of an electron is based on how much energy the electron has.

According to the modern atomic model, at atom has a small positively charged nucleus surrounded by a large region in which there are enough electrons to make an atom neutral.