Lecture 09 Nuclear Physics Part 1

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Lecture 09

Nuclear Physics Part 1

Structure and Size of the Nucleus

Νuclear Masses Binding Energy

The Strong Nuclear Force

Lecture 09

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Structure of the Nucleus

Discovered by Rutherford, Geiger and Marsden in 1909 (see lecture 2) Nucleus consists of protons and neutrons.

Terminology:

Refer to a nucleus with a given numbers of neutrons and protons as a nuclide

Z=Atomic Number (number of protons) N=Neutron number (number of neutrons) A=Mass number

A=Z+N (9.1)

Neutrons and protons are known as nucleons X

A Z

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Nuclear Size

Rutherford used α-particles of energy 7.7 MeV. What is the de Broglie wavelength of the α-particles ?

m 10 18 . 5 10 28 . 1 10 63 . 6 kgms 10 1.28 10 602 . 1 10 7 . 7 10 66056 . 1 4 2 10 602 . 1 10 7 . 7 10 66056 . 1 4 2 2 15 19 34 1 19 -19 6 27 19 6 27 2 2 − − − − − − − − × = × × = = × = × × × × × × × = × × × = × × × = = p h p p m p KE

λ

De Broglie wavelength of particle which becomes scattered gives approximate size of object under investigation.

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Further scattering by electrons, protons and neutrons at varying energies gives nuclear radius

A

V

R

V

A

R

∝

=

3 15 -3 1

sphere

a

of

Volume

m

10 1fm

(9.2)

fm

2 .

1

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Typical nuclear size 10-14_{m, typical atomic size 10}-10_m

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Nucleon Masses

Masses expressed in terms of unified mass constant (u) Mass of atom defined to be exactly 12u

Proton, neutron, electron masses:

C

12 6 2 27 - _kg _931.5 MeV 10 66056 . 1 c u = × = 2 31 2 27 2 27 MeV 0.511 u 000549 . 0 kg 10 109 . 9 MeV 939.57 u 008665 1 kg 10 6750 . 1 MeV 938.28 u 007276 1 kg 10 67264 . 1 c m c . m c . m e n p = = × = = = × = = = × = − − −

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Atomic masses in the periodic table are weighted averages over different isotopes.

Eg Chlorine isotopes with relative abundance:

35.5u

0.246 37u

0.754 35u

Chlorine

of

mass

Atomic

(24.6%)

Cl

and

(75.4%)

Cl

37₁₇ 35 17

=

×

+

×

=

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Question

What is the mass density of a typical nucleus, eg ?16₈

O

water! of density the times 10 than More kgm 10 3 . 2 10 16 . 1 ) 10 6606 . 1 )( 16 ( Density m 10 16 . 1 ) 2 . 1 ( 3 4 3 4 volume Sphere 14 3 -17 43 27 3 43 3 3 × = × × = = × = = = − − − u V M A R V ρ π

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[

]

well. as cancels on contributi mass electron The instead. them use we so masses nuclear than measure easier to are masses Atomic atom H neutral of mass atom, X neutral of mass mass, neutron (9.4) BE nucleus stable the of mass the and nucleons separated the of mass tal between to difference mass BE energy, binding (9.3) 2 A Z 2 = = = − + = = ∆ = ∆ ∆ = ∆ H m m m c m Nm Zm X m E mc E X n x n H

Some of the mass has been converted to energy

needed to bind the nucleus together !

Binding Energy

mass

neutron

mass

proton

mass

Nuclear

<

Z

×

+

N

×

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Question

(a) What is the binding energy of ?

(b) What is the binding energy per nucleon ?

C

12 6

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Overall shape can be explained by fission and fusion (coming later!) fission

fusion

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Compare Ionisation and Nuclear

Binding Energies

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Nuclear Energy Levels

From quantum mechanics of atoms, we know that atoms

with Z=2,10,18,36,54… are stable because sub-shells and shells are filled.

Nucleons are also spin-1/2 particles and are arranged in discrete energy levels.

Values of Z or N of magic numbers:2,8,20,28,50… lead to stable nuclei due to filled energy levels.

Nuclei with magic Z and N are particularly stable eg:

Pb

and

Ca

Ca,

O,

He,

16₈ 40₂₀ 48₂₀ 208₈₂ 4 2

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Segré Chart

>3000 known nuclei but < 300 stable

80

120

Z

40

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The Strong Nuclear Force

Q) Why do the protons which make up the nucleus not repel

each other sufficiently to cause the nucleus to disintegrate ? Where does the binding energy come from ?

A) There is another force at work in the nucleus and which is not apparent at larger distance scales : the strong nuclear force

Q) Can we use our fundamental quantum mechanics knowledge to find out about its properties ?

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Nucleons transmit the strong force to each other through the exchange of another particle, the pion.

nucleon _nucleon

pion

From Heisenberg’s Uncertainty principle, energy ∆E can be Borrowed for a time ∆t, as long as .

This allows the pion to be created and exist long enough to be exchanged.

h E t >

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(

)

m 10 9 10 1 . 3 10 3 t force of Range speed a at ed transmitt be cannot force The s 10 1 . 3 10 3 10 2.4 10 63 . 6 n interactio of Time borrowed energy of Amount kg 10 2.4 MeV/ 135 mass Pion 15 23 8 23 2 8 28 -34 2 -28 2 − − − − × = × × × = ∆ = > × = × × × × = = = × = = c c E h t c M E c M

This explains why the strong force is not significant outside of the nucleus!

A more sophisticated approach gives the range at 6x10-16 _m, which is roughly the radius of a nucleon.