nuclear chemistry chapter 21 nuclear chemistry nuclear chemistry the nucleus remember that the...

NuclearChemistry

Chapter 21Nuclear Chemistry

NuclearChemistry

The Nucleus

• Remember that the nucleus is comprised of the two nucleons, protons and neutrons.

• The number of protons is the atomic number.• The number of protons and neutrons together

is effectively the mass of the atom. (We will look at this in more detail later.)

NuclearChemistry

The Nucleus

• Remember that the nucleus is comprised of the two nucleons, protons and neutrons.

• The number of protons is the atomic number.• The number of protons and neutrons together

is effectively the mass of the atom.

Also considered to be the nuclear charge.

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Isotopes

• Not all atoms of the same element have the same mass due to different numbers of neutrons in those atoms.

• There are three naturally occurring isotopes of uranium:Uranium-234Uranium-235Uranium-238

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• There are three types of Radioactivity:

1. Spontaneous Decay

2. Nuclear Fission

3. Nuclear Fusion

Radioactivity

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Spontaneous Decay

• It is not uncommon for some nuclides of an element to be unstable, or radioactive.

• We refer to these as radionuclides.

• There are several ways radionuclides can decay into a different nuclide.

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Alpha Decay:

Loss of an -particle (a helium nucleus)

He42

U23892

Th23490 He4

2 +

NuclearChemistry

Alpha Decay:

Note how to balance a nuclear equation (even easier than a chemical equation):

U23892

Th23490 He4

2 +

NuclearChemistry

Alpha Decay:

Note how to balance a nuclear equation (even easier than a chemical equation):

U23892

Th 23490 He4

2 +

Total on top = 238

NuclearChemistry

Alpha Decay:

Note how to balance a nuclear equation (even easier than a chemical equation):

U23892

Th23490 He4

2 +

Total on top = 238

Total on top = 238

NuclearChemistry

Alpha Decay:

Note how to balance a nuclear equation (even easier than a chemical equation):

U23892

Th 23490 He4

2 +

Total on bottom = 92

NuclearChemistry

Alpha Decay:

Note how to balance a nuclear equation (even easier than a chemical equation):

U23892

Th23490 He4

2 +

Total on bottom = 92

Total on bottom = 92

NuclearChemistry

Alpha Decay:

Note how to balance a nuclear equation (even easier than a chemical equation):

U23892

Th23490 He4

2 +

Total on top = 238

Total on top = 238

Total on bottom = 92

Total on bottom = 92

NuclearChemistry

Typical Balancing Problem:

Note how to balance a nuclear equation (even easier than a chemical equation):

Ra22688

X?? He4

2 +

NuclearChemistry

Typical Balancing Problem:

Note how to balance a nuclear equation (even easier than a chemical equation):

Ra22688

X?? He4

2 +

Total on top = 226

Total on bottom = 88

NuclearChemistry

Typical Balancing Problem:

Note how to balance a nuclear equation (even easier than a chemical equation):

Ra22688

X?? He4

2 +

Total on top = 226

Total on top = 226

Total on bottom = 88

Total on bottom = 88

NuclearChemistry

Typical Balancing Problem:

Note how to balance a nuclear equation (even easier than a chemical equation):

Ra22688

X22286 He4

2 +

Total on top = 226

Total on top = 226

Total on bottom = 88

Total on bottom = 88

NuclearChemistry

Typical Balancing Problem:

Note how to balance a nuclear equation (even easier than a chemical equation):

Ra22688

Rn22286 He4

2 +

Total on top = 226

Total on top = 226

Total on bottom = 88

Total on bottom = 88

NuclearChemistry

Beta Decay:

Loss of a -particle (a high energy electron)

0−1 e0

−1or

I13153 Xe131

54 + e0

−1

n p + e10

11 -1

0

NuclearChemistry

Beta Decay:

Loss of a -particle (a high energy electron)

0−1 e0

−1or

I13153 Xe131

54 + e0

−1

53 p, 78 n

NuclearChemistry

Beta Decay:

Loss of a -particle (a high energy electron)

0−1 e0

−1or

I13153 Xe131

54 + e0

−1

53 p, 78 n 54 p, 77 n

NuclearChemistry

Beta Decay:

Loss of a -particle (a high energy electron)

0−1 e0

−1or

I13153 Xe131

54 + e0

−1

53 p, 78 n 54 p, 77 n

Good for decreasing the ratio of neutrons to protons!

NuclearChemistry

Positron Emission:

Loss of a positron (a particle that has the same mass as but opposite charge than an electron)

e01

C116

B115 + e0

1

Anti-matter!

NuclearChemistry

Positron Emission:

Loss of a positron (a particle that has the same mass as but opposite charge than an electron)

e01

C116

B115 + e0

1

p n + e11

10 1

0

NuclearChemistry

Positron Emission:

Loss of a positron (a particle that has the same mass as but opposite charge than an electron)

e01

C116

B115 + e0

1

6 p, 5 n 5 p, 6 n

NuclearChemistry

Positron Emission:

Loss of a positron (a particle that has the same mass as but opposite charge than an electron)

e01

C116

B115 + e0

1

6 p, 5 n 5 p, 6 n

Good for increasing the ratio of neutrons to protons!

NuclearChemistry

Gamma Emission:

Loss of a -ray (high-energy radiation that almost always accompanies the loss of a nuclear particle)

00

NuclearChemistry

Gamma Emission:

Loss of a -ray (high-energy radiation that almost always accompanies the loss of a nuclear particle)

00Sometimes shown to emphasize energy transfer, but not necessary for balancing.

NuclearChemistry

Electron Capture (K-Capture)

Addition of an electron to a proton in the nucleusAs a result, a proton is transformed into a

neutron.

p11 + e0

−1 n1

0

NuclearChemistry

Electron Capture (K-Capture)

Addition of an electron to a proton in the nucleusAs a result, a proton is transformed into a

neutron.

p11 + e0

−1 n1

0

Opposite of Beta Decay.

Good for increasing the ratio of neutrons to protons!

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More Balancing Examples:

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More Balancing Examples:

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Neutron-Proton Ratios

• Any element with more than one proton (i.e., anything but hydrogen) will have repulsions between the protons in the nucleus.

• A strong nuclear force helps keep the nucleus from flying apart.

NuclearChemistry

Neutron-Proton Ratios

• Neutrons play a key role stabilizing the nucleus.

• Therefore, the ratio of neutrons to protons is an important factor.

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For smaller nuclei (Z 20) stable nuclei have a neutron-to-proton ratio close to 1:1.

NuclearChemistry

Neutron-Proton Ratios

As nuclei get larger, it takes a greater number of neutrons to stabilize the nucleus.

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Stable Nuclei

The shaded region in the figure shows what nuclides would be stable, the so-called belt of stability.

NuclearChemistry

Stable Nuclei

• Nuclei above this belt have too many neutrons.

• They tend to decay by emitting beta particles.

NuclearChemistry

Stable Nuclei

• Nuclei above this belt have too many neutrons.

• They tend to decay by emitting beta particles.

Good for decreasing the ratio of neutrons to protons!

NuclearChemistry

Stable Nuclei

• Nuclei below the belt have too many protons.

• They tend to become more stable by positron emission or electron capture.

NuclearChemistry

Stable Nuclei

• Nuclei below the belt have too many protons.

• They tend to become more stable by positron emission or electron capture.

Good for increasing the ratio of neutrons to protons!

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Stable Nuclei

• There are no stable nuclei with an atomic number greater than 83.

• These nuclei tend to decay by alpha emission.

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Stable Nuclei

• Heavy atoms have too many protons repelling.

• They tend to become more stable by alpha emission.

No major change in the ratio of neutrons to protons! There will be a slight increase.

NuclearChemistry

Stable Nuclei

• Heavy atoms have too many protons repelling.

• They tend to become more stable by alpha emission.

Example: If have 150 n and 100 p, lose an alpha particle and will have 148 n and 98 p. Ratio rises from 1.50 to 1.51.

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Radioactive Series

• Large radioactive nuclei cannot stabilize by undergoing only one nuclear transformation.

• They undergo a series of decays until they form a stable nuclide (often a nuclide of lead).

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Some Trends

Nuclei with an even number of protons and neutrons tend to be more stable than nuclides that have odd numbers of these nucleons.

NuclearChemistry

Some Trends

Nuclei with 2, 8, 20, 28, 50, or 82 protons or 2, 8, 20, 28, 50, 82, or 126 neutrons tend to be more stable than nuclides with a different number of nucleons.

NuclearChemistry

Some Trends

Nuclei with 2, 8, 20, 28, 50, or 82 protons or 2, 8, 20, 28, 50, 82, or 126 neutrons tend to be more stable than nuclides with a different number of nucleons.

These are called Magic Numbers!

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Nuclear Fission

Nuclear transformations can be induced by accelerating a particle and colliding it with the nuclide.

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Particle Accelerators

These particle accelerators can be enormous, having circular tracks with paths that are miles long.

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Nuclear Fusion

• Combine two small atoms to make a larger one.

H + H He21 1

2 24

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Kinetics of Radioactive Decay

• Nuclear transmutation is a first-order process.

• The kinetics of such a process, you will recall, obey this equation:

= -kt Nt

N0

ln

NuclearChemistry

Kinetics of Radioactive Decay

• Nuclear transmutation is a first-order process.

• The kinetics of such a process, you will recall, obey this equation:

= -kt Nt

N0

ln

Chemical Reaction Equivalent:

ln[A]t

[A]o

= -kt

NuclearChemistry

Kinetics of Radioactive Decay

• Nuclear transmutation is a first-order process.

• The kinetics of such a process, you will recall, obey this equation:

= -kt Nt

N0

ln

For the Nuclear Version, you can use the following:

1. Number of Nuclei

2. Mass of Sample

3. Disintegrations per second

NuclearChemistry

Kinetics of Radioactive Decay

• The half-life of such a process is:

= t1/2 0.693

k

• Comparing the amount of a radioactive nuclide present at a given point in time with the amount normally present, one can find the age of an object.

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Measuring Radioactivity

• One can use a device like this Geiger counter to measure the amount of activity present in a radioactive sample.

• The ionizing radiation creates ions, which conduct a current that is detected by the instrument.

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Kinetics of Radioactive Decay

A wooden object from an archeological site is subjected to radiocarbon dating. The activity of the sample that is due to 14C is measured to be 11.6 disintegrations per second. The activity of a carbon sample of equal mass from fresh wood is 15.2 disintegrations per second. The half-life of 14C is 5715 yr. What is the age of the archeological sample?

NuclearChemistry

Kinetics of Radioactive Decay

First we need to determine the rate constant, k, for the process.

= t1/2 0.693

k

= 5715 yr 0.693

k

= k 0.693

5715 yr

= k 1.21 10−4 yr−1

NuclearChemistry

Kinetics of Radioactive Decay

Now that we know k, we can determine t:

= -kt Nt

N0

ln

= -(1.21 10−4 yr−1) t 11.615.2

ln

= -(1.21 10−4 yr−1) t ln 0.763

= t 2230 yr

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Energy in Nuclear Reactions

• There is a tremendous amount of energy stored in nuclei.

• Einstein’s famous equation, E = mc2, relates directly to the calculation of this energy.

• It would be more appropriate to think of this equation as E = mc2 .

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Energy in Nuclear Reactions

• In the types of chemical reactions we have encountered previously, the amount of mass converted to energy has been minimal (too small to detect).

• However, these energies are many thousands of times greater in nuclear reactions.

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Example Nuclear Decay:

Loss of an -particle (a helium nucleus)

He42

U23892

Th23490 He4

2 +

NuclearChemistry

Energy in Nuclear Reactions

The mass change for the decay of 1 mol of uranium-238 is −0.0046 g.

The change in energy, E, is then

E = (m) c2

E = (−4.6 10−6 kg)(3.00 108 m/s)2

E = −4.1 1011 J

NuclearChemistry

Energy in Nuclear Reactions

The mass change for the decay of 1 mol of uranium-238 is −0.0046 g.

The change in energy, E, is then

E = (m) c2

E = (−4.6 10−6 kg)(3.00 108 m/s)2

E = −4.1 1011 J

Notice mass must be in kg.

NuclearChemistry

Energy in Nuclear Reactions

For example, the mass change for the decay of 1 mol of uranium-238 is −0.0046 g.

The change in energy, E, is then

E = (m) c2

E = (−4.6 10−6 kg)(3.00 108 m/s)2

E = −4.1 1011 JCompare to chemical reactions, typically a few hundred kJ.

NuclearChemistry

Energy in Nuclear Reactions

For example, the mass change for the decay of 1 mol of uranium-238 is −0.0046 g.

The change in energy, E, is then

E = (m) c2

E = (−4.6 10−6 kg)(3.00 108 m/s)2

E = −4.1 1011 JIn WebAssign, enter only positive energies.

NuclearChemistry

How did we calculate this mass Change?

It appears that mass is conserved when balancing!

U23892

Th23490 He4

2 +

Total on top = 238

Total on top = 238

NuclearChemistry

How did we calculate this mass Change?

We need more exact masses when calculating energy changes!

U23892

Th23490 He4

2 +

Total on top = 238

Total on top = 238

238.0003 g 233.9942 g 4.0015g

NuclearChemistry

How did we calculate this mass Change?

We need more exact masses when calculating energy changes!

U23892

Th23490 He4

2 +

Total on top = 238

Total on top = 238

238.0003 g 233.9942 g 4.0015g

m = final mass – initial mass = -0.0046 g

NuclearChemistry

Nuclear Binding Energy

A helium nucleus consists of 2 protons and 2 neutrons, so mass should be:

massHe = 2(massneutron) + 2(massproton)

massHe = 2(1.00866 amu) + 2(1.00728 amu)

Predicted massHe = 4.03188 amu

True massHe = 4.00150 amu

NuclearChemistry

Nuclear Binding EnergyPredicted massHe = 4.03188 amu

True massHe = 4.00150 amu

Difference = 0.03038 amu

This difference is called the mass defect.

1 g = 6.022 x 1023 amu, so:

Difference = 5.045 x 10-26 g

E = 4.533 x 10-12 J = Binding Energy

NuclearChemistry

Nuclear Binding EnergyE = 4.533 x 10-12 J = Binding Energy

To fairly compare nuclei, want binding energy per nucleon, so

4.533 x 10-12 J / 4 nucleons

= 1.13 x 10-12 J / nucleon

NuclearChemistry

Nuclear Binding EnergyE = 4.533 x 10-12 J = Binding Energy

To fairly compare nuclei, want binding energy per nucleon, so

4.533 x 10-12 J / 4 nucleons

= 1.13 x 10-12 J / nucleon

Note: For 1 mole of He nuclei,

binding energy = 2.730 x 10+12 J

NuclearChemistry