nuclear chemistry (selected topics) introduction and important terms –very different than any...

Nuclear Chemistry (selected topics)

• Introduction and Important Terms– Very different than any other kind of “chemistry”!

• Spontaneous Nuclear Decay Reactions– Which nuclides decay, and how do they decay? (Zone /

Valley of stability)

• Conservation “Laws” of all Nuclear Reactions (How to complete a nuclear decay reaction equation)

• Kinetics of Nuclear Decay Reactions– Review of 1st order kinetics

• E=mc2, and relation to binding energy and mass defect; & “Binding energy per nucleon”

1

I. Introduction and Important Terms

• Chemical Reactions? (up till now)– New substances are made through the formation

of new nanoscopic “units” by making and/or breaking chemical bonds (Dalton)

– All the “action” is outside of the nuclei• Nuclei remain unchanged!• Chemical Bonding involves moving electrons, not nuclei

• Nuclear chemistry: Complete opposite!– It’s all about changing the nucleus!– Independent of any “standard” chemical reactions

2

From PS10 Sheet: Review of Terms

• Nucleon: a particle that’s part of the nucleus (i.e., either a proton (p) or neutron (n))

• Atomic Number (Z): # p’s in nucleus– Defines “who you are” (which element)

• Mass number (A): sum of p’s & n’s– **Not a “mass”; a (whole) number– Similar to nuclear mass (to nearest amu)

• Isotopes (of an element)– Have same number of protons, but different number of

neutrons. E.g., C-14 (8 n’s) vs C-12 (6 n’s)

• Complete atomic symbol of an isotope:

3

A

ZX

New Terms

• Nuclide: a nucleus with a specified number of neutrons (almost synonymous with “isotope”)– Refers more to the “thing” rather than the “type of matter”

• Radioactive Nuclide: a nuclide that undergoes a spontaneous nuclear decay process– With a corresponding release of some energetic particle (or

photon)

• Radiation: general (historic) term for the kind of energetic particles (or photons) that are emitted from a sample containing radioactive nuclides. Many kinds:– Alpha, beta, gamma, positron

• Stable Nuclide*: a nuclide that does not undergo any spontaneous nuclear decay process. *more on “stable” later

4

Other Nuclear Reactions(not all nuclear reactions are decay!)

5

• Spontaneous Nuclear Decay (discussed first)– Radioactive nuclides (only)– one (“reactant”) nuclide turns into another nuclide– not initiated (just happens)

• Other nuclear reactions (later)– Generally involve initiation & more than one

nuclide as “reactants”.• Fission and Fusion• Transmutation (bombardment) reactions

Two kinds of “stability” in this unit!

• One refers to whether a nuclide will undergo spontaneous nuclear decay.– Does the nuclide decay (unstable,

radioactive) or not (stable)?– The “valley of stability”

Kinetic Stability

Thermo-dynamic Stability

6

• One refers to how stable one nuclide is compared to another, in terms of “overall configuration of nucleons”– Applies to all nuclides, radioactive or not– Assessed by Binding energy per nucleon

(later)

Ex. 206Pb is a stable nuclide. 238U is radioactive

Ex. 56Fe is more stable than 206Pb or 2H

II. Nuclear Decay Reactions

• Compare and contrast the various kinds of nuclear decay types and their associated particles

• Symbolically represent nuclides and particles in a nuclear reaction equation

• Determine the “daughter” nuclide of a particular decay process if given the parent nuclide– Using two conservation rules (mass # and charge)

• Predict the likely decay process of a nuclide by using the “Valley of Stability” and related ideas

7

Objectives

Kinds of Nuclear Decay (and kinds and symbols of particles)

A. Alpha () decay [loss of an particle]

8

42He 4

2or

Apply conservation of mass # and charge*:

238 = ? + 4 ? = (= mass number)

92 = ? + 2 ? = (= “charge” [# of protons])

23490Th

What is the nuclide formed? (or complete the eqn)

*Note: Unlike what we do with ions, charge of nuclei or nuclear particles is represented by the lower left subscript. Why?

234

90

decay α23892 U α 4

2__

Kinds of Nuclear Decay (and kinds and symbols of particles)

B. Beta() decay [emission of a particle]

9


131 = ? + 0 ? = (= mass number)

53 = ? + -1 ? = (= “charge” [# of protons])

13154Xe


*Note: Charge of nuclei or nuclear particles is represented by the lower left subscript.

131

54

decay 13153 I e__

A high-energy electron ( or e)

0-1

Take a step back…what’s really happening in decay?

A neutron is turning into a _______!

10

11 p decay 1

0 n e_ 0-1

proton

13154Xe decay 131

53 I e__ 0-1

NOTE: The electron in decay is produced by the process (it is not a pre-existing electron)

Kinds of Nuclear Decay (What else can happen?)

11

C. Gamma radiation [emission of a particle]

A high-energy photon

• Photon = “particle” of light (no mass)

• “Repacking” of a nucleus

• An “excited” nucleus “relaxes” to lower energy, with an emission of a photono Not unlike an electron in an atom

• Usually happens after another nuclear reaction


12

C. Gamma radiation [emission of a particle]

A high-energy photon

• Basically, nothing appears to happen!

234 radiation 234 090 90 0* + Th Th


D. Positron emission [emission of a positron]

13


30 = ? + 0 ? = (= mass number)

15 = ? + 1 ? = (= “charge” [# of protons])

3014Si


30

14

30 . .15P P E 0

+1__ e

A “positive electron”, 0

1e

Take a step back…what’s really happening in positron emission?

A proton is turning into a neutron!

14

10 n1 . .

1p P E e_ 0+1

NOTE: A proton will not decay this way spontaneously unless it is in certain nuclei. Free protons are “stable”.

3014Si30 . .

15P P E 0+1__ e

A comment on “antimatter”

• Antimatter is real!

15

0 0-1 +1 "energy"e e

• It is true that “when matter meets antimatter, they mutually annihilate one another to form pure energy”

• A positron is a type of antimatter; an electron is a type of (regular) matter.

Kinds of Nuclear Decay (Guess what? There is a second way to turn a p into a n!)

E. Electron Capture

16

73 Li

7 0 . .4 -1Be + E Ce 0

0

• Different than the others

• “Added particle” is a reactant (not “produced”)

• A preexisting electron (inner shell) gets “snagged” by the nucleus (?!)

__

Overview: Table 19.1 in Tro (partial)

Ppt 06 Nuclear Chemistry 17

Overview: Table 19.1 in Tro (2nd part)


Nuclear Stability Patterns—The Valley of Stability

• How can we predict which kinds of nuclear decays occur in which nuclides?– Is there a pattern?

• Yes! But let’s start by looking at which nuclides are stable.– NOTE: I will not be explaining why these

ones are stable. This is, primarily, empirical.

19Ppt 06 Nuclear Chemistry

Nuclear Stability Patterns—The Valley of Stability

• Make a plot of number of neutrons (N) vs number of protons (Z) for stable nuclides– This “defines” the so-called “valley of

stability” (also “zone” or “belt” of stability)

• See board first. Then figures.


Ppt 06 Nuclear Chemistry

The stable nuclides lie in a very narrow band of neutron-to-proton ratios.

Nuclei that lie below the band don't have enough neutrons and are therefore neutron-poor.

The ratio of neutrons to protons in stable nuclides gradually increases as the number of protons in the nucleus increases.

Light nuclides, such as 12C, contain about the same number of neutrons and protons.

Heavy nuclides, such as 238U, contain up to 1.6 times as many neutrons as protons.

There are no stable nuclides with atomic numbers larger than 83.

This narrow band of stable nuclei is surrounded by a sea of instability.

Nuclei that lie above the band have too many neutrons and are therefore neutron-rich.

22


http://en.wikipedia.org/wiki/File:Isotopes_and_half-life.svg

NOTE: The farther away a

nuclide is from the valley of stability, the shorter its half life.

“Farther = less (kinetically) stable”

Table 19.2 Number of Stable Nuclides with Even and Odd Numbers of Nucleons


Even numbers (of nucleons) appear to correlate with stability. Theory of nucleon energy levels is beyond the scope of this course (and my knowledge!)

More from the web…

• http://en.wikipedia.org/wiki/Isotope

• http://atom.kaeri.re.kr/

25

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

http://atom.kaeri.re.kr/

26

Figure 18.16 (Zumdahl) A Plot of (Potential) Energy versus the Separation Distance (particles = protons)

18–26Ppt 06 Nuclear Chemistry

Using The Valley of Stability to Predict “Which decay?”

• See board


Summary of Strategy for Predicting Decay Type

• First determine if “above, below, or beyond” the valley of stability:– If Z > 83, it is “Beyond”

• Not always “correct”, but correct prediction

– If Z ≤ 83, Figure out if the nuclide has:• “too many neutrons” (“Above”) OR• “too few neutrons” (“Below”)

– (NOTE: long way or shortcut way*; even if you use shortcut, be able to relate it to the n/p ratio!)

• Then make conclusion by noting which process makes daughter closer to the “valley” (next slide)

28

*Discussed later

Summary of Strategy for Predicting Decay Type (continued)

• It turns out that…A radioactive nuclide tends to decay in such a way that its daughter nuclide is closer to the valley of stability

• decay turns n to p used by nuclides above valley (“neutron rich”)

• PE or EC turns p to n used by nuclides below valley (“neutron poor”)

• decay lose both n and p used by nuclides beyond valley (too many of both)

29

How to determine if a nuclide is “above”, “below”, or “beyond”?

• Long way: – Calculate n/p (=N/Z) ratio– Compare actual n/p ratio to ~stable n/p ratio:

• Know that for Z = 1-20, n/p = 1 is ~stable• Know that for Z = ~80, n/p = 1.5 is ~stable• Know that for Z ~40, n/p ~1.25 is stable

• Short way: (next slide)

30

(if you don’t have a valley of stability table)

“Above, Below, or Beyond?”(continued)

• Short way (makes some assumptions, but…): Compare A to “aam”

A is the mass number of the isotope; “aam” = average atomic mass of element

o If A > aam, predict “too many neutrons”o If A < aam, predict “too few neutrons”

• Why does this work?– It is likely to be the case that the most abundant

isotopes on Earth are “stable”. – Thus, the average atomic mass, if rounded, is likely to

be close to the mass number of nuclides near the valley of stability!

31

Examples

• See handout sheet and board examples

32

Nuclear Decay Kinetics

• See board first

33


Table 18.3 The Half-Lives of Nuclides in the 238

92U Decay Series

34


Table 18.4 Syntheses of Some of the Transuranium Elements

35


Figure 18.3 The Decay of a 10.0-g Sample of Strontium-90 Over Time

36


Figure 18.4 The Half-Lives of Radioactive Nuclides

Figure 18.7 Geiger-Muller Counter

Rates of nuclear reactions (“activities”) can be directly measured using a Geiger counter.

38

Table 19.6 Some Radioactive Nuclides, with Half-Lives and Medical Applications as

Radiotracers


Bone Scan (using gamma ray emissions of Tc-99m)


Energy-related Issues

• See Board– Consider a nucleus of an atom of U-238– How much mass do you think it should

contain?– How about a whole atom of U-238?

• mass of a proton = 1.007276 amu• mass of a neutron = 1.008665 amu• mass of an electron = 0.00054858 amu


Important Clarification

• Note: Although binding energy technically refers to the E required to separate a nucleus into free nucleons, and thus “mass defect” represents the difference between the “mass of free nucleons” and the “mass of the nucleus”, the way we calculate mass defect from mass data usually involves a slightly different quantity because experimentally it is the mass of an atom that is known, not the mass of “just” the nucleus. [next page]

42

To calculate Mass Defect From “mass data”…(rationalizing Tro’s approach)

• Let mass defect be abbreviated mmd

mmd = mass of free nucleons – mass of nucleus

= m(p’s + n’s) – m(nucleus)

m(p’s + e’s + n’s) – m(nucleus + e’s)

= m(H atoms + n’s) – m(atom)

This “works” because the energy lowering associated with binding the electrons to the nucleus (electrostatic force at large distance) is almost negligible relative to the energy lowering associated with binding the nucleons to one another (strong force at small distance)

43

Tro

bonded bonded

EXAMPLE 19.7 Mass Defect and Nuclear Binding Energy Calculate the mass defect and nuclear binding energy per nucleon (in MeV) for C-16, a radioactive isotope of carbon with a mass of 16.014701 amu.

SOLUTION

© 2011 Pearson Education, Inc.

*Tro’s solution disappoints me! I want you to be able to use E = mc2! Otherwise there’s little “learning value” IMO. So:

amu 1

kg 10 x 1.6605 x amu 0.118879

-27

m (in kg)

Calculate the mass defect as the difference between the mass of one C-16 atom and the sum of the masses of 6 hydrogen atoms and 10 neutrons.

Calculate the nuclear binding energy by converting the mass defect (in amu) into MeV.(Use 1 amu = 931.5 MeV.)*

mc2 (in J)

2

s

m 10 x 2.9979x

8

converts to MeV

9..MeV2110.7J 10 x 1.6022

MeV 1x

13-

*Means atomic mass here, not nuclear mass!

*

= m(H atoms + n’s) – m(atom) [prior slide]

EXAMPLE 19.7 Mass Defect and Nuclear Binding Energy

Calculate the nuclear binding energy by converting the mass defect (in amu) into MeV.(Use 1 amu = 931.5 MeV.)*

Determine the nuclear binding energy per nucleon by dividing by the number of nucleons in the nucleus.

Calculate the mass defect and nuclear binding energy per nucleon (in MeV) for C-16, a radioactive isotope of carbon with a mass of 16.014701 amu.

Calculate the mass defect as the difference between the mass of one C-16 atom and the sum of the masses of 6 hydrogen atoms and 10 neutrons.

SOLUTION

© 2011 Pearson Education, Inc.

To calculate Mass Defect From “mass data”…(Mines method in some answer keys)

• Let mass defect be abbreviated mmd

mmd = mass of free nucleons – mass of nucleus

= m(p’s + n’s) – m(nucleus)

m(p’s + n’s) – [m(atom) – m(e’s)]

I used to find this way easier to “follow” (students tend to find it odd that you use the mass of an H atom instead of the mass of a proton), but I’ve recently switched in lecture to Tro’s way (despite what I wrote in some past answer keys).

46

Binding Energy per nucleon indicates the thermodynamic stability of a nucleus

• Although we typically think that being “low in (potential) energy” is associated with more stability, that isn’t quite so for nuclei.– The different number of nucleons in different nuclei

make Eb an “unfair” comparison.

• Dividing Eb by the number of nucleons (Eb per nucleon) allows for a fair comparison!– It’s like comparing the price of two boxes of cereal,

one with 11 oz and one with 16 oz. If you find the “price per ounce” you can tell which is the better buy!

47

6 He-5 nuclei

3 Be-10 nuclei

2 N-15 nuclei

1 Mg-30

nucleus


If separated nucleons had zero potential energy, the nuclides (bound nucleons) would have negative potential energy (lower than zero).

What is the "lowest energy" way to combine 30 nucleons?

-300

-250

-200

-150

-100

-50

0

0 1 2 3 4 5

E

(M

eV)

[fro

m f

ree

nu

cleo

ns]

6 He-5's

3 Be-10's

2 N-15's1 Mg-30


NOTE: I’m assuming zero for potential energy of separated nucleons.

Does it continue this way if we consider combining larger amounts of nucleons?

Say, six times more (i.e., 240)?

50

What is the "lowest energy" way to combine 240 nucleons?

-2500

-2000

-1500

-1000

-500

0

0 3.801 7.602

E

(M

eV)

[fro

m f

ree

nu

cleo

ns]

4 Ni-60's2 Cd-120's

1 Cm-240

48 He-5's

24 Be-10's

16 N-15's8 Mg-30's



Figure 18.9 The Binding Energy per Nucleon as a Function of Mass Number


Figure 18.10 Both Fission and Fusion CAN Produce More Stable Nuclides and are thus Exothermic

Spontaneous IF nuclide is very large; (fusion of large nuclides would be endothermic!!)

Spontaneous IF nuclide is small. (fission of small nuclides would be endothermic!!)


Figure 18.11 Fission


Figure 18.12 Fission Process in which each Event Produces Two Neutrons


Figure 18.13 Result of Too Small a Mass of Fissionable Material

nuclear chemistry (selected topics) introduction and important terms –very different than any...

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