Lecture 30 – Chapter 22, Sections 1-2 Nuclear Stability and Decay

• Energy Barriers

• Types of Decay

• Nuclear Decay Kinetics

What reacts first?

• If we have a solution of sodium chloride in water, and we pass electricity through it, what gets reduced and what gets oxidized?

1. Identify species present: Na+(aq) Cl–

(aq) H2O (l)

2. Identify half-reactions with only those species as reactants. Na+

(aq) + e– Na (s) – 2.71 VCl–

(aq) + e– Cl2–(aq) Not Possible

2 H2O (l) + 2 e– H2 (g) + 2 OH–(aq) – 0.828 V

3. The reaction that will be driven first is the one that is most nearly spontaneous – has the least negative E.

In this case we will generate H2 gas, not Na metal.

What About Oxidation?1. Identify species present: Na+

(aq) Cl–(aq) H2O (l)

2. Identify half-reactions with only those species as reactants. Na+

(aq) Na (s) + e– Not Possible2 Cl–

(aq) Cl2 (g) + 2 e– – 1.35827 VCl– + 9 H2O 6 H3O+ + ClO3

– + 6 e– – 1.451 VCl– + 12 H2O 8 H3O+ + ClO4

– + 8 e– – 1.389 V2 H2O 2 H3O+ + H2O2 + 2 e– – 1.776 V6 H2O 4 H3O+ + O2 + 4 e– – 1.229 V

3. The reaction that will be driven first is the one that is most nearly spontaneous – has the least negative E.

It looks like we will make O2 gas.But, making Cl2 gas and making ClO4

– are very close.In these situations, kinetics becomes important. Since chlorine gas

production only needs 2 electrons and the others need 4 and 8, it turns out that chlorine gas is mostly what gets produced.

Nuclear Chemistry

Stability

• If it is so energetically favorable to add nucleons to a nuclide, why doesn’t every nucleus just keep getting bigger?

• Electrostatics!

• For nuclei r is very, very small• So, this presents a tremendous barrier to an incoming charged

nuclide

• Neutrons are a little more complicated.

rqqkE ticelectrosta

21=

Who’s Law is This?

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rqqkE ticelectrosta

21=

20%20%20%20%20% 1. Coulomb’s

2. Einstein’s3. Joule’s4. Krueger’s5. Newton’s

More Stability

• Large nuclei tend to have a larger number of stable isotopes• H and He have two, F one• Sn has ten• # protons ≈ # neutrons for small nuclei

– Protons and neutrons tend to pair up• # neutrons a bit greater than # protons for larger nuclei

– This helps to reduce the Coulombic repulsion between protons

The Middle Way

• The strong nuclear force is many-body. This means that 3 particles (per particle) are actually held together more strongly than two particles (per particle).– Bottom line is that larger nuclei are more stable (per

particle) than smaller nuclei• However, large nuclei become unstable because of Coulombic

repulsion.• So, there is a middle ground where these effects balance

– Iron is the most stable nucleus.

Iron = Stable

• Smaller nuclei merge together to make larger ones– FUSION

• Larger nuclei fall apart to become smaller– FISSION

Nuclear Decay

• When nuclei spontaneously change from one nuclide to another, we call this decay

• Nuclides that are particularly unstable are radioactive• Nuclear reactions are very similar to chemical reactions

– Mass Number is conserved (protons + neutrons), though mass is not because of E = mc2.

– Charge is conserved

• For instance:

– Note that sum of superscripts of reactants = products (Mass Number)– And sum of subscripts of reactants = products (Charge)

epn 01

11

10 −+→

Nuclear Decay Processes

• Variety of processes are possible when nuclei decay• Some involve particle emission• Some involve particle absorption• Some involve energy emission

Alpha Radiation• Alpha particles are energetic helium nuclei (4

2He)• Very heavy positively charged particles• Not too dangerous• Can be stopped by fabric or a couple of sheets of paper

• Mass number of emitter decreases by 4• Atomic number of emitter decreases by 2• Occurs to nuclei that are unstable because they are too large

(too many total particles)

α

α42

21482

21884

42

21884

22286

+→

+→

PbPoPoRn

Belt of Stability

Beta Radiation

• Beta particles are electrons (0-1β–)

• Very penetrating• Beta decay occurs to nuclei that lie above the belt of stability.

– These nuclei have ‘too many’ neutrons– Beta decay converts neutron to proton

−−

−−

−−

+→

+→

+→

β

β

β

01

20880

20879

01

32

31

01

11

10

HgAuHeH

pn

Belt of Stability

Positron Radiation

• Positrons are anti-electrons (0+1β+)

• Very penetrating• Positron decay occurs to nuclei that lie below the belt of

stability. – These nuclei have ‘too many’ protons– Positron decay converts proton to neutron

+

+

+

+→

+→

+→

β

β

β

01

14462

14463

01

188

189

01

10

11

EuNdOF

np

Belt of Stability

More Positron

• Positrons are not usually observed directly• When a positron and electron run into each other they annihilate

– Usually there are lots of electrons around, so this happens right away

– Annihilation destroys both particles (no more mass), but releases loads of energy

– Energy released as two gamma rays, each of 9.87 × 107 kJ/mol

Electron Capture

• Absorption of electron by the nucleus• Electron removed from 1s orbital – leaves a ‘hole’• This hole is filled by an outer electron falling down

– Electron releases energy as an X-ray photon• Like positron decay, electron capture occurs to nuclei that lie

below the belt of stability. – Electron capture converts proton to neutron

rayXhMgMgMgeAl

−

−

+→

→+

ν2612

*2612

*2612

01

2613

Gamma Radiation

• Electromagnetic photons of very high energy• Very penetrating can pass through the human body• Require thick layers of lead or concrete to be stopped• Emitted from nuclei that have excess energy

– Usually from products of other nuclear decay

γ

α

γ

α

+→

+→

+→

+→

PoPoPoRn

RnRnRnRa

m

m

m

m

21884

21884

42

21884

22286

22286

22286

42

22286

22688

Sometimes metastable(m) is denoted with a * meaning just ‘excited’

Identify the Product

α ? 21484 +→Po

20%20%20%20%20% 1. Polonium-210

2. Lead-2123. Lead-2104. Mercury-2125. Mercury-210

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Identify the product

? 21083

21082 +→ BiPb

20%20%20%20%20% 1. Alpha particle

2. Beta particle3. Positron4. Gamma Ray5. X-Ray

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Rates of Decay

• Recall from Chapt 15 that nuclear decay is unimolecular– First Order– Rate = k × concentration (or often # of nuclei)

21

21

2lnln

2ln

ln

0

0

0

tt

NN

kt

ktcc

ecc kt

=

=

=

= −

Today• Read Chapter 22• REVIEW REVIEW REVIEW!!!• Go to biology or physics seminar

Monday• Work on CAPA #17