radiochemistry dr nick evans n.d.m.evans@lboro.ac.uk

Radiochemistry

Dr Nick Evansn.d.m.evans@lboro.ac.uk

Why Radiochemistry?

Radioisotopes are widely used in:1. Diagnostic and therapeutic nuclear medicine

• 500 000 per annum2. Mechanistic and kinetic studies of reactions 3. Analysis4. Agriculture5. Industry

Why?1. Ease and sensitivity of detection of radioisotopes2. Automation of counting of radioisotopes3. Availability of radioisotopes

Theory of Atomic Structure

• Atom = nucleus + extra-nuclear electrons• Nucleus = neutrons and protons held together by

“strong interactions”• Strong nuclear force (interaction) is a

fundamental force of nature which affects only quarks, antiquarks, and gluons

• Range of force is about 10-15 m• Strong enough to overcome Coulombic repulsion

of protons

Potential Energy of Proton near Nucleus

0

PE

Distance from nucleus (r)

Range of attractive Nuclear Force

Coulombic Repulsion

Binding Energy of Nucleus

• Indication of how strongly the nucleus is bound together

• Energy liberated in formation of nucleus from its nucleons is a measure of its stability

• High binding energy = stable nucleus• Sum of individual masses of nucleons is different

to mass of nucleus, e.g. for 168O

Binding Energy of Nucleus (2)

• On 12C scale:– Mass of proton = 1.007825 amu– Mass of neutron = 1.008665 amu– Mass of electron = 0.0005485 amu

• Thus:– 8 protons = 8.0626– 8 neutrons = 8.06932– 8 electrons = 0.004388– Sum = 16.136308

• Actual mass of 16O on 12C scale = 15.9949148• Therefore, mass defect = 0.141394 amu

Binding Energy of Nucleus (3)• Decrease in mass is due to energy release

when atom is formed, i.e.:• E = mc2

= 0.141394 x 10-3 kg x (3 x 108 ms-1)2/6.023 x 1023

= 2.1128 x 10-11 J

• But 1 eV = 1.6021 x 10-19 J• Thus E = 131.9 MeV

or = 8.24 MeV per nucleon• Sun loses 4.2 million tonnes per second as it

builds heavier nuclei• Plot binding energy per nucleon vs. mass number

Binding Energy per Nucleon vs. Mass Number

5

6

7

8

9

0 50 100 150 200 250

Mass Number

Bin

din

g E

ne

rgy

per

Nu

cle

on

(M

eV)

Fission releases energyFusion

releases energy

Fission releases energyFusion

releases energy

Binding Energy per Nucleon

• The most stable elements have mass numbers around 56, specifically

• 8 MeV is high energy compared with electromagnetic radiation – UV is a few electron volts (eV) to ~100 eV– X-ray photons have energies ~100 eV to ~100 keV– Gamma-ray energies > 100 keV

• Small peaks represent particularly stable nuclei– high binding energy per nucleon

5626Fe

4 16 28 42 88 2082 8 14 20 38 82He, O, Si, Ca, Sr, Pb etc.

Separation Energy

• Energy required to remove a single neutron from the nucleus

• Shows the stability of nuclei built from α-particles• Mass increasing in jumps of 4

Neutron Separation Energies

He-4

He-5

Li-6Li-7

Be-8

Be-9

B-10

B-11

C-12

C-13

N-14N-15

O-16

O-17

F-18F-19

Ne-20

Ne-21

Ne-22

Na-23

Mg-24

Mg-25

Al-26

Al-27

Si-28

Si-29

P-30P-31

S-32

-2

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

Atomic Number

Neu

tron

Sep

arat

ion

Ener

gy (M

eV)

Magic Numbers• Leads to concept of ‘magic numbers’ for certain numbers

of neutrons and protons• Suggests there are energy levels in the nucleus• Equivalent to idea of full outer shell of electrons in noble

gases• Magic Nos.: 2, 8, 20, 28, 50, 82, 126• Nuclei with this number of protons, or neutrons or sum of

the 2 which is a magic number are especially stable, e.g.4

2He, 168O, 40

20Ca, 20882Pb

Nuclear Energy Levels

Two Theories of Nuclear Structure:

• Liquid drop model• Assumes nucleons behave like molecules in a liquid

• random movement and exchange of position• Scattering experiments suggest that nuclei have

approximately constant density (2.4 x 1014 g cm-3)• Takes into account that the forces on nucleons on surface

are different from those in interior where the nucleons are completely surrounded by others

• Like taking into account surface tension of liquid drop

Nuclear Energy Levels (2)

• Shell Model• Accounts for energies of particles emitted• Dense-gas type models of nuclei with multiple

collisions between particles didn't fit data• Patterns like magic numbers suggest shell

structure

Nuclear Energy Levels

• Analogous to filled electron shells• No principal quantum number• Levels are determined by angular momentum

quantum number• Jumps between levels caused by absorption or

emission of energy• Often gamma

Neutron : Proton Ratio

• Approximately 275 nuclei have shown no evidence of radioactive decay

• ~60% of these have:• even numbers of protons and• even numbers of neutrons

• In general the most abundant on earth

• Remaining ~40% are about equally divided between:

• even number of protons and odd number of neutrons• odd number of protons and even number of neutrons

Neutron : Proton Ratio (2)

• There are only 4 ‘stable’ nuclei with an odd number of protons and neutrons:

• 21H, 6

3Li, 105B, 14

7N,

• Relative abundances of 0.015, 7.42, 19.6, 99.63%• Very light nuclei

• Elements of even atomic number have more stable isotopes than those of odd atomic number

• Occurs due to energy stabilisation of pairs of protons and/or neutrons

The Stable Region

• Stability is favoured by even numbers of protons and neutrons

• Not usually equal numbers• Plotting neutron number (A) against proton

number (Z) for all known nuclei, shows area of stability

• For very light elements N ≈ Z gives stable elements

• 1:1 up to 4020Ca

• Ratio gradually rises (A>Z) until by element 83 (Bi, the last one with a stable isotope) it is ~1.5

The Stable Region (2)

• If the N/P ratio is too high for stability then isotope is neutron rich • likely to decay by β- emission

• If the N/P ratio is too low for stability then isotope is proton rich• likely to decay by β+ emission or electron

capture

Stable Isotopes

0

20

40

60

80

100

120

140

0 10 20 30 40 50 60 70 80 90

Atomic Number (Z)

Mas

s N

umbe

r (A)

Neutron-rich areaβ- decay favoured

Proton-rich areaβ+ or EC decay favoured

Nuclei Showing Ground State Energy (MeV)

61Zn56765

62Zn57692

63Zn58623

64Zn59550

65Zn60482

60Cu55832

61Cu56760

62Cu57690

63Cu58619

64Cu59551

59Ni54898

60Ni55826

61Ni56758

62Ni57686

63Ni58619

58Co53967

59Co54896

60Co55829

61Co56759

62Co57692

57Fe53036

58Fe53965

59Fe54898

60Fe55829

61Fe56763

Stable Isotopes

61Zn56765

62Zn57692

63Zn58623

64Zn59550

65Zn60482

60Cu55832

61Cu56760

62Cu57690

63Cu58619

64Cu59551

59Ni54898

60Ni55826

61Ni56758

62Ni57686

63Ni58619

58Co53967

59Co54896

60Co55829

61Co56759

62Co57692

57Fe53036

58Fe53965

59Fe54898

60Fe55829

61Fe56763

Mass = 61 Isobar

Fe

Co

Ni

Cu

Zn

-2

0

2

4

6

8

10

25 26 27 28 29 30 31

Atomic Number

Mas

s D

iffe

ren

ce (

MeV

)

Normally only 1 nucleus per mass number is stable