Option C Nuclear Physics, Radioactive decay and half life

1. http://lawrencekok.blogspot.com
Prepared by
Lawrence Kok
Tutorial on Atomic Structure, Particle Physics and Relative Atomic
Mass.

2. Video on scale of universeExcellent Flash on biological cellsExcellent Flash on scale of universe
Atomic Structure
Atomic Size radius
•Order of magnitude – (10-10
– 10-12
)m
•Radius Li atom – (1.5 x 10-10
)m
•Radius nucleus – (1 x 10-14
)m
Scale of matter from smallest to largest
1nm – 1 x 10-9
m
1pm – 1 x 10-12
m
1A - 1 x 10-10
m
Radius Li
atom
Radius Nucleus
Li atom
Elementary particles making up
nucleon (protons + neutrons)
Nucleon - (proton + neutron)
Proton – 2 up quark + 1 down quark
Neutron – 2 down quark + 1 up quark
Unit conversion

3. Video on new particles physics
Atomic Structure
Atomic Size radius
•Order of magnitude – (10-10
– 10-12
)m
•Radius Li atom – (1.5 x 10-10
)m
•Radius nucleus – (1 x 10-14
)m
1nm – 1 x 10-9
m
1pm – 1 x 10-12
m
1A - 1 x 10-10
m
Radius Li
atom
Radius Nucleus
Li atom
Elementary particles making up
nucleon (protons + neutrons)
Unit conversion
Structure within atom
Discovery particles with help of Large Hadron Collider
Nucleon - (proton + neutron)
Proton – 2 up quark + 1 down quark
Neutron – 2 down quark + 1 up quark

4. Higgs Boson Discovery Wins Nobel Prize for Physics
Video on Higgs field part 2
Video on Higgs field part 1
Video on timeline discovery
Structure within atom
Video on new particles physics
Recent discovery particles from
Large Hadron Collider
Higgs boson leftover excitation of particles of Higgs field
Discovery of Higgs boson and Higgs field
Particles interact with Higgs field to produce mass
Video on NOBEL PRIZE 2013 !!!!!!
Discovery timeline to Quantum model Discovery of elementary particles Elementary particles

5. Video (Minute physics)Video (Ted Talk)Video (RI)Video (Veratasium)
Video on Higgs field
Elementary particles
Structure within atom
Recent discovery particles from
Large Hadron Collider
Higgs boson leftover excitation
of particles of Higgs field
Discovery of Higgs boson and Higgs field
Particles interact with Higgs field to produce mass
Mass (proton + neutron)- due to interaction bet
up quarks/down quarks with gluons (energy fluatution)
Proton -2 up quarks
1 down quark
Neutron -1 up quark
2 down quarks
What is Higgs Boson ?
What is Higgs Field ?
Excellent videos –Particles interact with Higgs field create MASS

6. Nuclear reaction vs Chemical reaction
Nuclear rxn
Involve proton/neutron in nucleus
Decomposition of nucleus into smaller nuclei
Energy released greater
Conservation of charge/atomic mass number
Chemical rxn
Involve outer most electron
Transfer/sharing/loss of electron
Energy released less
Conservation of mass and charge
2Na + CI2  2NaCI
Type
radiation
Nature
radiation
Symbol Penetration
(mass,m/charge,e)
Ionising
power
(removing
electron)
Alpha Helium
nucleus
α Low ratio
(high m/e)
High
Beta High energy
electron
β Moderate Moderate
Gamma High frequency
electromagnetic
radiation
γ High ratio
(small m/e)
Low
Type of radiation
Nuclear equation- decay of nucleus Chemical equation – valence electron
Transfer electrons
Sharing electrons

7. Nuclear rxn
Alpha Decay
Losing an alpha particle – helium nucleus
Daughter nuclei lower in proton number
Mass of 4 (2 proton + 2 neutron)
+2 charged (only 2 protons) = +2
Decay of uranium, thorium, actinium
Beta Decay
Losing beta particle –Electron/positron
Daughter nuclei higher in proton number
Negative charge (-1)
Decay neutron  proton + electron
Alpha Decay Beta Decay
Gamma Decay
Gamma decay
Losing γ particle - EM radiation high frequency
Daughter nuclei no change in atomic mass
α β
Unstable nucleus atom Decay by emitting ionizing particles
+

8. Video on γ decayVideo on β decayVideo on α decay
Alpha, Beta, Gamma Radiation
Alpha Decay
Lose alpha particle – helium nucleus
Mass He- 4 (2 proton + 2 neutron)
+2 charged (2 proton + 2 neutron + 0 e)
Daughter nuclei lower in proton number
Beta Decay
Lose beta particle –Electron/beta β
Negative charge (-1)
-1 charged (β / electron)
Daughter nuclei higher in proton number
Gamma decay
Lose γ particle –EM radiation of high frequency
Daughter nuclei no change in atomic mass
Nucleus > 84 proton
Unstable, radioactive decay
Decay depend ratio neutron/proton
Decay depend ratio neutron/proton
Neutron/proton ratio LOW – Proton rich
Decay to reduce proton
Alpha decay, α (proton number  )
Mass number alway Conserved
Decay depend ratio neutron/proton
Neutron/proton ratio HIGH – Neutron rich
Decay to reduce neutron
Beta decay β ( Neutron  Proton + electron)
Ratio decrease 
Decay depend ratio neutron/proton
Neutron/proton ratio HIGH /LOW
Gamma decay γ, is associated along
with Alpha and Beta

9. Radioactive
isotopes
Half-life
Uranium 238 4.5 x 109
Carbon-14 5.7 x 103
Radium-226 1.6 x 103
Strontium-90 28 years
Iodine-131 8.1 days
Bismuth-214 19.7
minutes
Polonium-214 1.5 x 10-4
Isotopes
Stable IsotopesUnstable Isotopes
Unstable Isotopes – emit radiation

RADIOISOTOPES
Simulation isotope 12
C, 13
C, 14
C
Radioisotopes
Half-life – time taken for
conc/amt/number/activity isotope
to fall to half of its original value.
Half life decay – always constant
Shorter half-life
More unstable, decay fast
Long half-life
More stable, decay slowly
Emit radiation form unstable isotope
Simulation isotope 1
H, 2
H, 3
H
Video on Half life
Simulation half life C-14/uranuim
Half-life
Conc/amt/number/activity

10. Carbon – 3 Isotopes
Radiocarbon/carbon dating
Half life C-14 = 5730 yr
Beta (β/electron ) decay
Conclusion
Ratio C14/C12 constant is organism alive
Ratio C14/C12 drop  organism die
Uses
Age dead organic fossil contain Carbon
Max age limit 60,000 yrs old.
Carbon -12 Carbon-14Carbon -13
Abundance – 99% (Stable) Abundance – 1% (Stable)
Abundance – trace amt
(Unstable , radioactive)
How is form?
• C-14 produce in stratosphere when
neutron hit nitrogen atom to form C-14
•C-14 to N-14 by converting neutron  proton
(proton stay in nucleus), electron emit as β radiation
• emit as β ray.
(proton in nucleus – increase proton number)
emit as β ray.
•Ratio C14/C12- constant if alive – TAKE in C14 (C12 constant)
•Ratio C14/C12- drop if dead - NOT taking C14. (C12 constant)
How it is form?

11. Radiocarbon/carbon dating
Half life C-14 = 5730 yr
Beta (β/electron ) decay
Carbon -14
Abundance – trace amt
(Unstable , radioactive)
How is form?
• C-14 produce in stratosphere when
neutron hit nitrogen atom to form C-14
•C-14 to N-14 by converting neutron  proton
(proton stay in nucleus), electron emit as β radiation
• emit as β ray.
(proton in nucleus – increase proton
number)
emit as β ray.
•Ratio C14/C12- constant if alive – TAKE in C14 (C12 constant)
•Ratio C14/C12- drop if dead - NOT taking C14. (C12 constant)
Video C-14 Carbon Dating Video C-14 Carbon Dating Video C-14 Half life Carbon Dating
Simulation C-14 (Half life)
At 100% (Starting)
Simulation C-14 (Half life)
At 50% (Starting)
Video Radiocarbon dating
Click to view simulation
How Radiocarbon dating work?

12. Video on Radio tracer
Radiocarbon/carbon dating
Half life C-14 = 5730 yr
Carbon -14
Beta (β/electron) decay
Video on C-14 Carbon Dating
Video Radiocarbon dating
How Radiocarbon dating work?
Uses of radioactive isotopes
Radiotherapy/cancer/tumour Tracers/studying metabolic pathways
Cobalt-60
Half life Co-60 = 5.27 yr Half life I-131 = 8 days
How Gamma rays works? How Radio tracer works?
Iodine-131
Sterilization – killing bacteria/germ
Radiotherapy – kill tumor cells
High energy electromagnetic ray
Gamma γ + β decay
Carbon dating
Age of fossil remains
Radio tracer
Trace pathway in body
Beta β (90%) and γ (10%) decay
Gamma γ + β decay

13. Radioactive decay Half life formula
t
A
A
o
t
λ−=
][
][
ln
t
t
t
o
t
eAA
e
A
A
λ
λ
−
−
=
=
0][][
][
][
λ
2ln
2/1 =t
2/1
5.0 t
t
oAA =
][. AdecayRate λ=
First order
n
oAA 5.0=
Final conc
Decay constant
Half life
Initial conc
Time
Half-life – time taken for
conc/amt/number/activity isotope
to fall to half of its original value.
Half life decay – always constant
Bismuth-212 half life 1 hr. How long take for 16 g sample to decay, so 1g remain
Time/h Mass left/g
0 16
1 8
2 4
3 2
4 1
Time = 4h
method 1 method 2
hrtime
e
e
A
A
t
t
o
t
4
16
1
][
][
693.0
=
=
=
−
−λ
693.0
1
693.0
2ln
2/1
==
=
λ
λ
t
Initial conc isotope sample is 1.4 10-6
M .Find half life, if conc left is 1.365 x 10-6
M after 2 hr
1
6
6
0126.0
2
]104.1[
]10365.1[
ln
][
][
ln
−
−
−
=
−=
×
×
−=
hr
t
A
A
o
t
λ
λ
λ
hrt
t
55
0126.0
2ln
2ln
2/1
2/1
==
=
λ
Number Half life

14. Radioactive decay Half life formula
t
A
A
o
t
λ−=
][
][
ln
t
t
t
o
t
eAA
e
A
A
λ
λ
−
−
=
=
0][][
][
][
λ
2ln
2/1 =t
2/1
5.0 t
t
oAA =
][. AdecayRate λ=
First order
n
oAA 5.0=
Final conc
Decay constant
Half life
Initial conc
Time
Number Half life
Rn half life 1620 yrs. Find decay constant, and deduce proportion of sample remain after 100yr
%8.95958.0
][
][
][
][
][
][
100000428.0
==
=
=
×−
−
o
t
o
t
t
o
t
A
A
e
A
A
e
A
A λ
1
2/1
000428.0
1620
693.0
2ln
−
==
=
hr
t
λ
λ
λ
2ln
2/1 =t
Rn half life 1622 yrs. Find how long it will take a sample to decay to 10% of its original sample
λ
2ln
2/1 =t
1
2/1
000427.0
1622
693.0
2ln
−
==
=
hr
t
λ
λ
yrstime
e
e
A
A
t
o
t
t
o
t
5392
%]100[
%]10[
][
][
000427.0
=
=
=
×−
−λ

15. t
A
A
o
t
λ−=
][
][
ln
t
t
t
o
t
eAA
e
A
A
λ
λ
−
−
=
=
0][][
][
][
λ
2ln
2/1 =t
2/1
5.0 t
t
oAA =
][. AdecayRate λ=
First order
n
oAA 5.0=
Final conc
Decay constant
Half life
Initial conc
Time
Piece wood found to have activity of 10 cpm g-1
of carbon .
New wood has count of 15 cpm g-1
. Half life C-14 is 5570 yr. Find
age of wood.
yrstime
e
e
A
A
t
o
t
t
o
t
3270
]15[
]10[
][
][
000124.0
=
=
=
×−
−λ
1
2/1
000124.0
5570
693.0
2ln
−
==
=
yr
t
λ
λ
λ
2ln
2/1 =t
Mass sample was measured, and re-measured 120 days later.
56% of original sample remain. Find half life
λ
2ln
2/1 =t
dayst
t
143
00483.0
693.0
2ln
2/1
2/1
==
=
λ
1
00483.0
120
%]100[
%]56[
ln
][
][
ln
−
=
×−=
−=
day
t
A
A
o
t
o
t
λ
λ
λ
Sample half life 0f 8hr has activity of 450 unit after 48hr. Find
original activity
2/1
5.0 t
t
oAA = n
oAA 5.0=
Number Half life
n = 48/8 = 6
unitA
A
AA
o
o
t
t
o
28846
5.0450
5.0
8
48
2/1
=
=
=
unitA
A
AA
o
o
n
o
28846
5.0450
5.0
6
=
=
=
Sr -90 half life of 28 yr. Find how much sample left after 280 yr
2/1
5.0 t
t
oAA = n
oAA 5.0=
Number Half life
n = 280/28 = 10
%098.0
5.0
5.0
28
280
2/1
=
=
=
o
o
t
t
o
A
A
AA
AA
%098.0
5.0
5.0
10
=
=
=
o
o
n
o
A
A
AA
AA
Radioactive decay Half life formula
Number Half life

16. yrstime
t
t
A
A
o
t
22460
000121.0
60
4
ln
][
][
ln
=
×−=
−= λ
% material decay
100% – 0.1% = 99.9% decay
Radioactive decay Half life formula
t
A
A
o
t
λ−=
][
][
ln
t
t
t
o
t
eAA
e
A
A
λ
λ
−
−
=
=
0][][
][
][
λ
2ln
2/1 =t
2/1
5.0 t
t
oAA =
][. AdecayRate λ=
First order
n
oAA 5.0=
Final conc
Decay constant
Half life
Initial conc
Time
Piece wood found to have activity of 6 cpm g-1
of carbon .
New wood has count of 15 cpm g-1
. Half life C-14 is 5280 yr. Find
age of wood.
yrstime
e
e
A
A
t
o
t
t
o
t
6980
]15[
]6[
][
][
000131.0
=
=
=
×−
−λ
1
2/1
000131.0
5280
693.0
2ln
−
==
=
yr
t
λ
λ
λ
2ln
2/1 =t
Fission product from nuclear shd be isolated for 10 half life. Find
fraction radioactive remain after this time.
Deduce % material decay in this time
C-14 in atmosphere produce 60 count hr-1
g-1
. Sample sea shell
found to have 4 count hr-1
g-1
. estimate age of shell. Half life C-
14 is 5730yr
Pu half life 88yr. Explain why activity sample is constant
over 1 yr. Find % sample remain after 20 yrs.
n
oAA 5.0=
Number Half life
n = 10
%1.0
5.0
5.0
10
=
=
=
o
o
n
o
A
A
AA
AA
remain
λ
2ln
2/1 =t
1
2/1
000121.0
5730
693.0
2ln
−
==
=
yr
t
λ
λ
1 yr short compare to half-life, 88 yr, Pu activity doesnt change much
λ
2ln
2/1 =t
1
2/1
007877.0
88
693.0
2ln
−
==
=
yr
t
λ
λ
854.0
][
][
][
][
][
][
20007877.0
=
=
=
×−
−
o
t
o
t
t
o
t
A
A
e
A
A
e
A
A λ
= 85.4 %
Number Half life

17. Acknowledgements
Thanks to source of pictures and video used in this presentation
http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/nucnot.html
http://www.m2c3.com/chemistry/VLI/M3_Topic2/M3_Topic2_print.html
http://www.universityneurosurgery.com/index.php?src
http://www.medwow.com/med/cobalt-linear-accelerator/radon/tr-cobalt-60/42865.model-spec
http://endocrinesurgery.ucla.edu/patient_education_adm_tst_radioactive_iodine_uptake_test.html
Thanks to Creative Commons for excellent contribution on licenses
http://creativecommons.org/licenses/
Prepared by Lawrence Kok
Check out more video tutorials from my site and hope you enjoy this tutorial
http://lawrencekok.blogspot.com