Radioactivity

Lecture 4 The Physics of radioactive Decay

and Nuclear Reaction

Nature of Radiation

• Deflection in electric field • α radiation is positively charged • β radiation is negatively charged • γ radiation is neutral • Stopping in material • α radiation has small range and

large mass • β radiation has deep range and

small mass • γ radiation has largest range and

no mass – electromagnetic radiation

Origin of Radiation • Radioactive decay of unstable nucleus

configuration (too many protons or too many neutrons) transitioning into a more stable form.

• What represents a stable or unstable isotope configuration

• Too many protons deflective Coulomb forces • Too many Neutrons reduce the strong binding

force • Too many nucleons cannot be bound together

by strong force • Too much deformation increases instability of

nucleus. • Heavy deformed nuclei will spontaneously

fission

Radiation as Energy Release A nucleus emits radiation of certain energy (E=hν for gammas and E=Ekin for particles) to reach the lowest possible energy configuration!

2

2 1 mvEkin =

Energy release in gravitational potential

Energy release in nuclear potential

Particle decay to excited states with subsequent de-excitation by emission of gamma radiation

β-decay

γ-decay

γ-spectrum

β- decay n ⇒ p+e-+ν

β+ decay p ⇒ n+e++ν

_

Alpha Decay of the Nucleus

Occurs mainly for very heavy nuclei which are not stable against alpha emission

Alpha particle α = 4He

88 226

86 222

2 4Ra Rn He⇒ +

Nucleus conversion through α-decay

Determine the end-product of the ‘yellow’ a-emitter: Z A

N Z A

NX X⇒ +− −

−2 4

2 α

Z

N

Beta Decay of the Nucleus

β decay is the emission of an electron e- or positron e+ to convert a neutron to a proton or a proton to a neutron inside the nucleus 6 · e+  7 · e+ +1 · e-

The β decay always converts along isobars

Too many neutrons

Too many protons

Gamma Decay of Nucleus

excited states in nucleus

Excitation of nucleus with subsequent characteristic γ emission

Excited states correspond to vibration, rotation or quantum state excitation

Ex

γ emission l< 10-15 m

Nucleus conversion through β+,--decay

Z A

N Z A

N

Z A

N Z A

N

X X X X

⇒ +

⇒ + − +

+

+ − −

1 1

1 1

β

β Determine the end-product of the β+-emitter:

Determine the end-product of the β--emitter:

Z

N

Energy in Nuclei According to Einstein’s formula, each nucleus with a certain mass m stores energy: E=mc2

Proton mp = 1.007596 · 1.66·10-24 g = 1.672·10-24 g Neutron mn = 1.008486 · 1.66·10-24 g = 1.674·10-24 g Carbon m12C = 12.00000 · 1.66·10-24 g = 1.992·10-23 g Lead m208Pb = 207.797665 · 1.66·10-24 g = 3.449·10-22 g Uranium m238U = 238.050783 · 1.66·10-24 g = 3.952·10-22 g

1 amu=1/12(m12C)=1.66 · 10-24 g Breaking up nuclei into their constituents requires energy

www.nndc.bnl.gov/chart/reCenter.jsp?z=42&n=53

http://amdc.impcas.ac.cn/web/masseval.html

http://amdc.impcas.ac.cn/evaluation/data2012/data/mass.mas12 http://www.nndc.bnl.gov/chart/reCenter.jsp?z=42&n=53 http://amdc.impcas.ac.cn/web/masseval.html

Some unavoidable unit considerations

227

23

19

2

2

/49.9311066.11 /300000

10022.6 106022.11

11

cMeVkgamu skmc

particlesgA JeV

s mkgJ

=⋅=

= ⋅≡

⋅=

⋅ =

−

−

http://en.wikipedia.org/wiki/Electronvolt

http://en.wikipedia.org/wiki/Electronvolt http://en.wikipedia.org/wiki/Electronvolt http://en.wikipedia.org/wiki/Electronvolt http://en.wikipedia.org/wiki/Electronvolt http://en.wikipedia.org/wiki/Electronvolt

Nuclear binding energy

M · c2 < Z mp · c2 + N mn · c2

The mass difference is the binding energy B

The binding energy is the energy that needed to dissociate a nucleus into its single constituents. It is released when N neutrons and Z protons fusion together to form a nucleus with the mass number A!

The mass M of the nucleus is smaller than the mass of its proton and neutron constituents!

E=m·c2 N=3 neutrons

Z=3 protons

Calculating the Nuclear Binding Energy

B = (Z · mp+ N · mn- M) · c2 Binding energy B of nucleus ( ) ( ) ( ) ( )

( )

( ) nucleon

J A

CB

J s mkg

s mgsmg

smggg

cmmmCB Cnp

12 12

11 2

11 2

821625

28232424

212

1017.1

10404.110404.110404.1/1091056.1

/10310992.110674.1610672.16

66 12

−

−−−−

−−−

⋅=

⋅=  

  ⋅=

 

  ⋅=⋅⋅⋅=

=⋅⋅⋅−⋅⋅+⋅⋅=

⋅−⋅+⋅=

( ) ( ) ( ) ( )

( )

( ) nucleon

J A

UB

J s mkg

s mgsmg

smggg

cmmmUB Unp

12 238

10 2

10 2

721624

28222424

2238

10145.1

10725.210725.210725.2/1091003.3

/10310952.310674.114610672.192

14692 238

−

−−−−

−−−

⋅=

⋅=  

  ⋅=

 

  ⋅=⋅⋅⋅=

=⋅⋅⋅−⋅⋅+⋅⋅=

⋅−⋅+⋅=

Nuclear Potential and internal forces

( ) ( )

MeVaMeVaMeVaMeVaMeVa oddNZAoddNZAaevenNZAa

A ZAaAZZaAaAaB

psymcsv

pp

symcsv

34;23;72.0;8.16;5.15

);(0);,();,(

21

3/43/4

2 3/13/2

=====

+==⋅−=⋅+=

+ −

⋅−⋅−⋅⋅−⋅−⋅=

−−

−

δδδ

δ

http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 1 MeV = 1.602·10-13 J

http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2

Nuclear Binding Energy Components

Mass number

1 MeV = 1.602·10-13 J

Binding energy normalized to mass number B/A B /A

(M eV

/n uc

le on

)

Example: What is the binding energy of the oxygen isotope 18O?

mp= 1.007596 · 1.66 · 10-24 g mn= 1.008486 · 1.66 · 10-24 g

M(18O) = 17.99916 · 1.66 · 10-24 g

Z=8, N=10, A=18

Atomic Mass Unit: 1 amu=1/12(M12C)=1.66 · 10-24 g

B = (Z · mp+ N · mn- M) · c2 B(18O) = 1.382 · 105 keV = 2.21·10-11 J B(18O)/A=1.23·10-12 J

1g 18O contains 7.41·1011 J (W·s)

Nuclear Decay Processes

A ⇒ B+b A(b)B

14C(β-ν)14N 234U(α)230Th

Decay energy is released in kinetic energy of emitted particles or in electromagnetic gamma radiation energy

( )

JeVMeVQ

MeVMeVMeVMeVQ

BBBQBBBQ cmcmmQ

U

U

ThHeUUAbBd

AbBd

127

22

104.81025.55.52

5.52128.12755296.28325.1779

234

234

2304234234

−⋅=⋅==

=−+=

−+=−+= ⋅−⋅+= JeV 19106.11 −⋅=

Nuclear Reactions and Energy Release

a

A

Frederic Joliot and Irene Curie at Paris had observed the first nuclear reaction. Enrico Fermi showed the existence of neutron induced reactions, which produce artificial radioactivity.

Nuclear reactions can produce energy Q > 0 exothermic or need energy Q < 0 endothermic

A(a,b)B Q = (mA+ ma- mB- mb)·c2

Q = BB+ Bb- BA-BB

Nobel Prize 1938

Difference of masses in entrance and exit channel determines Q

Q value of nuclear reaction process

a

A

b

B

A+a ⇒ B+b

A(a,b)B

projectile

target

product

recoil ( ) ( ) ( ) ( )

reactioncendothermi0 reactionexothermic0

22

< >

+−+= ⋅+−⋅+=

Q Q

BBBBQ cmmcmmQ

aAbB

aAbB

Example: Nuclear Reaction energy budget

isotope B (J)

2H 3.34131·10-13

4He 4.53297·10-12 12C 1.47643·10-11

119Pd 1.59643·10-10

238U 2.88631·10-10

( )

JJJQ UBPdBPdBQ

QPdU

JJJQ HBHB