Atoms ,Molecules and Nuclei

Prepared by physics dept

Sangita Holkar

The Atom

The atom consists of two parts:

1. The nucleus which contains:

2. Orbiting electrons.

protons

neutrons

All matter is made up of elements (e.g. carbon,

hydrogen, etc.).

The smallest part of an element is called an atom.

Atom of different elements contain different numbers of

protons.

The mass of an atom is almost entirely due to the

number of protons and neutrons.

The Atom

XA

Z

Mass number

Atomic number

Element symbol

= number of protons + number of neutrons

= number of protons

XA

Z

A = number of protons + number of neutrons

Z = number of protons

A – Z = number of neutrons

Number of neutrons = Mass Number – Atomic Number

U235

92U

238

92

There are many types of uranium:

A

Z

Number of protons

Number of neutrons

A

Z

Number of protons

Number of neutrons

U235

92U

238

92

There are many types of uranium:

Isotopes of any particular element contain the same

number of protons, but different numbers of neutrons.

A 235

Z 92

Number of protons 92

Number of neutrons 143

A 238

Z 92

Number of protons 92

Number of neutrons 146

Most of the isotopes which occur naturally are stable.

A few naturally occurring isotopes and all of the man-

made isotopes are unstable.

Unstable isotopes can become stable by releasing

different types of particles.

This process is called radioactive decay and the

elements which undergo this process are called

radioisotopes/radionuclides.

Radioactive decay results in the emission of either:

• an alpha particle (a),

• a beta particle (b),

• or a gamma ray(g).

Radioactive Decay

An alpha particle is identical to that of a helium nucleus.

It contains two protons and two neutrons.

Alpha Decay

XA

ZY

A - 4

Z - 2+ He

4

2

Alpha Decay

unstable atom

more stable atom

alpha particle

Alpha Decay

Ra226

88

Rn222

86

He4

2

XA

ZY

A - 4

Z - 2+ He

4

2

Ra226

88Rn

222

86+ He

4

2

Alpha Decay

Rn222

86He

4

2+Po

218

84He

4

2

Rn222

86+Y

A

ZHe

4

2

Alpha Decay

He4

2U

234

92+Th

230

90He

4

2

XA

Z+Th

230

90He

4

2

Alpha Decay

Th230

90+Y

A

ZHe

4

2

Alpha Decay

He4

2+Ra

226

88He

4

2Th

230

90

XA

Z+Pb

214

82He

4

2

Alpha Decay

He4

2+Pb

214

82He

4

2Po

218

84

Beta Decay

A beta particle is a fast moving electron which is

emitted from the nucleus of an atom undergoing

radioactive decay.

Beta decay occurs when a neutron changes into a

proton and an electron.

Beta Decay

As a result of beta decay, the nucleus has one less

neutron, but one extra proton.

The atomic number, Z, increases by 1 and the mass

number, A, stays the same.

Beta Decay

Po218

84

b0

-1

At218

85

XA

ZY

A

Z + 1+ b

0

-1

Beta Decay

Po218

84Rn

218

85+ b

0

-1

Th234

90Y

A

Z+ b

0

-1

Beta Decay

Th234

90Pa

234

91+ b

0

-1

XA

ZPb

210

82+ b

0

-1

Beta Decay

Tl210

81Pb

210

82+ b

0

-1

Bi210

83Y

A

Z+ b

0

-1

Beta Decay

Bi210

83Po

210

84+ b

0

-1

XA

ZBi

214

83+ b

0

-1

Beta Decay

Pb214

82Bi

214

83+ b

0

-1

Gamma Decay

Gamma rays are not charged particles like a and b

particles.

Gamma rays are electromagnetic radiation with high

frequency.

When atoms decay by emitting a or b particles to form a

new atom, the nuclei of the new atom formed may still

have too much energy to be completely stable.

This excess energy is emitted as gamma rays (gamma ray

photons have energies of ~ 1 x 10-12 J).

Radioactivity:

Lead

Box

Radioactive

substance

α

β

γ

-

-

-

--

-

-

--

-

-

+

+

+

+

+

+

+

+

+

+

Radioactivity is the phenomenon of emitting

alpha, beta and gamma radiations

spontaneously.

Soddy’s Displacement Law:

1. ZYA Z-2Y

A-4α

2. ZYA Z+1Y

Aβ

3. ZYA ZYA (Lower energy)

γ

Rutherford and Soddy’s Laws of Radioactive Decay:

1. The disintegration of radioactive material is purely a random process and

it is merely a matter of chance. Which nucleus will suffer disintegration, or

decay first can not be told.

2. The rate of decay is completely independent of the physical composition

and chemical condition of the material.

3. The rate of decay is directly proportional to the quantity of material

actually present at that instant. As the decay goes on, the original material

goes on decreasing and the rate of decay consequently goes on

decreasing.

If N is the number of radioactive atoms present at any instant, then the rate of

decay is,

dt

dN- α N or

dN

dt- = λ N

where λ is the decay constant or the disintegration constant.

Rearranging,

N

dN= - λ dt

Integrating, loge N = - λ t + C where C is the integration constant.

If at t = 0, we had N0 atoms, then

loge N0 = 0 + C

loge N - loge N0 = - λ t

or loge (N / N0) = - λ t

orN

= e- λt

N0

or N = N0 e- λ t No

. o

f ato

ms (

N) N0

N0/2

N0/4

N0/8N0/16

Time in half lives

0 T 2T 3T 4T

Radioactive Disintegration Constant (λ):

According to the laws of radioactive decay,

N

dN= - λ dt

If dt = 1 second, then

N

dN= - λ

Thus, λ may be defined as the relative number of atoms decaying per second.

Again, since N = N0 e- λ t

And if, t = 1 / λ, then N = N0 / e

orN0

N=

e

1

Thus, λ may also be defined as the reciprocal of the time when N / N0 falls to 1 / e.

Half – Life Period:

Half life period is the time required for the disintegration of half of the amount

of the radioactive substance originally present.

If T is the half – life period, then

N0

N=

2

1= e - λ T

e λ T = 2

(since N = N0 / 2)

λ T = loge 2 = 0.6931

T =λ

0.6931

T

λ = 0.6931

or

Time t in which material changes from N0 to N:

t = 3.323 T log10 (N0 / N)

Number of Atoms left behind after n Half – Lives:

N = N0 (1 / 2)t/TN = N0 (1 / 2)n or

Units of Radioactivity:

1. The curie (Ci): The activity of a radioactive substance is said to be one

curie if it undergoes 3.7 x 1010 disintegrations per second.

1 curie = 3.7 x 1010 disintegrations / second

2. The rutherford (Rd): The activity of a radioactive substance is said to be

one rutherford if it undergoes 106 disintegrations per second.

1 rutherford = 106 disintegrations / second

3. The becquerel (Bq): The activity of a radioactive substance is said to be

one becquerel if it undergoes 1 disintegration per second.

1 becquerel = 1 disintegration / second

1 curie = 3.7 x 104 rutherford = 3.7 x 1010 becquerel

Nuclear Fission:

Nuclear fission is defined as a type of nuclear disintegration in which a heavy

nucleus splits up into two nuclei of comparable size accompanied by a

release of a large amount of energy.

0n1 + 92U

235 → (92U236) → 56Ba141 + 36Kr92 +30n

1 + γ (200 MeV)

Chain Reaction:

n = 1

N = 1

n = 2

N = 9

n = 3

N = 27

Neutron (thermal) 0n1

Uranium 92U235

Barium 56Ba141

Krypton 36Kr92

n = No. of fission stages

N = No. of Neutrons

N = 3n

Chain Reaction:

n = 1

N = 1

n = 2

N = 9

n = 3

N = 27

Critical Size:

For chain reaction to occur, the

size of the fissionable material

must be above the size called

‘critical size’.

A released neutron must travel

minimum through 10 cm so that it

is properly slowed down (thermal

neutron) to cause further fission.

If the size of the material is less

than the critical size, then all the

neutrons are lost.

If the size is equal to the critical

size, then the no. of neutrons

produced is equal to the no. of

neutrons lost.

If the size is greater than the

critical size, then the reproduction

ratio of neutrons is greater than 1

and chain reaction can occur.

Nuclear Fusion:Nuclear fusion is defined as a type of nuclear reaction in which two lighter

nuclei merge into one another to form a heavier nucleus accompanied by a

release of a large amount of energy.

Energy Source of Sun:

Proton – Proton Cycle:

1H1 + 1H

1 → 1H2 + 1e

0 + 0.4 MeV

1H1 + 1H

2 → 2He3 + 5.5 MeV

2He3 + 2He3 → 2He4 + 2 1H1 + 12.9 MeV

Carbon - Nitrogen Cycle:

6C12 + 1H

1 → 7N13 + γ (energy)

7N13 → 6C

13 + 1e0 (positron)

Energy Source of Star:

6C13 + 1H

1 → 7N14 + γ (energy)

7N14 + 1H

1 → 8O15 + γ (energy)

8O15 → 7N

15 + 1e0 (positron)

7N15 + 1H

1 → 6C12 + 2He4 + γ (energy)

End of Atomic Nucleus

Nature of a wave

• A wave is described by frequency , wavelength , phase velocity u and intensity I

• A wave is spread out and occupies a relatively large region of space

Nature of a particle

• A particle is specified by mass m, velocity v, momentum p, and energy E

• A particle occupies a definite position in space.

In order for that it must be small

Light

• Interference and Diffraction experiments showed the wave nature of light

• Blackbody radiation and Photoelectric effectcan be explained only by considering light as a stream of particles

So is light a wave or a particle

?

How are they related?

E = h

• E– energy of the photon

• – frequency of the wave

• h– plank's constant

p=h/

p – momentum of the particle

- wavelength of the photon

40

DE BROGLIE HYPOTHESIS

LOUIS DE BROGLIE

“ If radiation which is basically a wave can exhibitparticle nature under certain circumstances, andsince nature likes symmetry, then entities whichexhibit particle nature ordinarily, should also exhibitwave nature under suitable circumstances”

In the Year 1924 Louis de Brogliemade the bold suggestion

The reasoning used might be paraphrased as follows

1. Nature loves symmetry2. Therefore the two great entities, matter and

energy, must be mutually symmetrical3. If energy (radiant) is undulatory and/or

corpuscular, matter must be corpuscular and/or undulatory

The de Broglie Hypothesis

• If light can act like a wave sometimes and like a particle at other times, then all matter, usually thought of as particles, should exhibit wave-like behaviour

• The relation between the momentum and the wavelength of a photon can be applied to material particles also

Prince Louis de Broglie (1892-1987)

de Broglie Wavelength

Relates a particle-like property (p) to a wave-like property ()

h

mv

43nm

VoltsVforthus

nmVV

getweeandmhforngsubstituti

meV

h

mE

hThen

VdifferencePotentialabydaccelerate

EEnergyKineticwithelectronanfor

mv

h

p

hwavelengthBrogliede

1226.0100

226.1

100

226.1

10602.11011.92

10625.6

,,

22

''

''

particle theof velocity theis v

particle theof mass theis m

Constant sPlanck' ish

1931

34

DE BROGLIE WAVELENGTH

The Wave associated with the matter particle is called Matter Wave.The Wavelength associated is called de Broglie Wavelength.

E hf

The frequency

• De Broglie postulated that all particles satisfy Einstein’s relation

ƒE

h

In other words,

Example: de Broglie wavelength of an electron

Mass = 9.11 x 10-31 kgSpeed = 106 m / sec

m10287m/sec) kg)(10 10(9.11

secJoules10636 10

631

34

.

.

This wavelength is in the region of X-rays

Example: de Broglie wavelength of a ball

• Mass = 1 kgSpeed = 1 m / sec

m10636m/sec) kg)(1 (1

secJoules10636 3434

..

Theoretical implication – The Bohr postulate

• Consider standing waves produced in a stretched string tied at two ends

Condition for these standing waves is that the length

of the string should be integral multiple of /2

The Diffraction

X-rays electrons

The diffraction patterns are similar because electrons have similar wavelengths to X-rays

Wave-like Behaviour of Matter

• Evidence: – electron diffraction

– electron interference (double-slit experiment)

• Also possible with more massive particles, such as neutrons and a-particles

• Applications:– Bragg scattering

– Electron microscopes

– Electron- and proton-beam lithography

particle wave function

Wave-Particle Duality

Wave Function

• Completely describes all the properties of agiven particle

• Called y y (x,t); is a complex function of position x and time t

particle wave function

Wave-Particle Duality

53

PHASE VELOCITY

Phase velocity: The velocity with which a wave travels is called Phase

velocity or wave velocity. It is denoted by vp. It is given by

v

cv p

2

Where c = velocity of light and v = is velocity of the particle.

The above equation gives the relationship between the phase velocity and

particle velocity.

It is clear from the above equation that, Phase velocity is not only greater

than the velocity of the particle but also greater than the velocity of light,

which can never happen. Therefore phase velocity has no physical

meaning in case of matter waves. Thus a concept of group velocity was

introduced.

54

GROUP VELOCITY

Since phase velocity has no meaning, the concept of group velocity was

introduced as follows.

“ Matter wave is regarded as the resultant of the superposition of largenumber of component waves all traveling with different velocities. The resultantis in the form of a packet called wave packet or wave group. The velocity withwhich this wave group travels is called group velocity.” The group velocity isrepresented by vg.

Vg

Particle

Vp

AIM OF EXPERIMENT

• To demonstrate diffraction phenomenon of electron to support wave character of material.

• This experiment gave establishment of quantum mechanics and schrodinger wave equation.

• The experiment consisted of firing an electron beam from an electron gun directed to a piece of nickel crystal at normal incidence (i.e. perpendicular to the surface of the crystal). The experiment included an electron gun consisting of a heated filament that released thermally excited electrons, which were then accelerated through a potential difference giving them a certain amount of kinetic energy towards the nickel crystal.

• To avoid collisions of the electrons with other molecules on their way towards the surface, the experiment was conducted in a vacuum chamber. To measure the number of electrons that were scattered at different angles, an electron detector that could be moved on an arc path about the crystal was used. The detector was designed to accept only elastically scattered electrons.

• As Max von Laue proved in 1912 the crystal structure serves as a type of three dimensional diffraction grating. The angles of maximum reflection are given by Bragg's condition for constructive interference from an array,Bragg'slaw

• for n = 1, θ = 50°, and for the spacing of the crystalline planes of nickel (d = 0.091 nm) obtained from previous X-ray scattering experiments on crystalline nickel.

This is 3-d grating of nickel target where scattering of electron takes place.

• By varying the applied voltage to the electron gun, the maximum intensity of electrons diffracted by the atomic surface was found at different angles. The highest intensity was observed at an angle θ = 50° with a voltage of 54 V, giving the electrons a kinetic energy of 54 eV.

• So this experiment proved de-brogliehypothesis and braggs equation.this also brought revolution in quantum mechanics.