2 X A Z Mass Number Atomic Number Element Symbol Atomic number (Z) = number of protons in nucleus...

2

XA

ZMass Number

Atomic NumberElement Symbol

Atomic number (Z) = number of protons in nucleus

Mass number (A) = number of protons + number of neutrons

= atomic number (Z) + number of neutrons

A

Z

1p1

1H1

or

proton

1n0

neutron

0e-1

0-1or

electron

0e+1

0+1or

positron4He2

42or

particle

1

1

1

0

0

-1

0

+1

4

2

Review

Nuclear EquationsNuclear Equations• The total number of protons and neutrons before a

nuclear reaction must be the same as the total number of nucleons after reaction.

• There are three main types of radiation which we consider: -Radiation is the loss of 4

2He from the nucleus,

-Radiation is the loss of an electron from the nucleus,

-Radiation is the loss of high-energy photon from the nucleus.

Copyright © Cengage Learning. All rights reserved.

20 | 4

• Symbols for other particles are given below:

γphoton Gamma

βor ePositron

βor eElectron

nNeutron

Por HProton

00

01

01

01-

01-

10

11

11

• In nuclear chemistry to ensure conservation of nucleons we write all particles with their atomic and mass

numbers: 42He and 4

2 represent -radiation.

6


20 | 7

• There are six common types of radioactive decay.

1. Alpha emissionEmission of an alpha particle from an unstable nucleus.


20 | 8

2. Beta emissionEmission of a beta particle from an unstable nucleus. Beta emission is equivalent to a neutron converting to a proton.


20 | 9

3. Positron emissionEmission of a positron particle from an unstable nucleus. Positron emission is equivalent to a proton converting to a neutron.


20 | 10

4. Electron captureThe decay of an unstable nucleus by capture of an electron from an inner orbital of the atom. Electron capture is equivalent to a proton converting to a neutron.


20 | 11

5. Gamma emissionEmission from an excited nucleus of a gamma photon, corresponding to radiation with a wavelength of approximately 10-12 m. Technetium-99m is an example of a metastable nucleus; it is in an excited state and has a lifetime of ≥ 10-9 s.


20 | 12

6. Spontaneous fissionThe spontaneous decay of an unstable nucleus in which a heavy nucleus of mass number greater than 89 splits into lighter nuclei and energy is released.

•Nucleons can undergo decay:

10n 1

1p+ + 0-1e

- (-emission)

10p

+ 10n + 01e

+ (positron or +-emission)

• A positron is a particle with the same mass as an electron but a positive charge.

0-1e- + 0

1e+ 200 (positron annihilation)

11p+ + 0

-1e- 10n (electron capture)

Types of Decay:

Alpha: (slowest moving; highest mass

23892 U He4

2 + Th23490

“parent” “daughter”

21183

Bi

Molecular view of the nuclear equation for the decay of uranium-

238

Beta: (e-) pe 11

0-1

10 n

I13153 Xe e 131

540

-1

Th23490

Gamma: (quite often occurs in conjunction with other decay processes)

Co6027

*Co6027

(extremely penetrating)

Molecular view of the nuclear equation for the decay of

technetium-99 (gamma emission)

Kelter, Mosher and Scott, Chemistry: The Practical Science, 1/e.

Positron emission:

or 0

1or 1

0e

enp 01

10

11

Tc 9543

e01 Mo95

42

PET Scan:

0-1e- + 0

1e+ 200 (positron annihilation)


technetium-95 (positron emission)

Figure 20.17: A patient undergoinga PET scan of the brain

Alexander Tsiara/ Photo Researchers, Inc.

Figure 20.16: PET scans of normal and schizophrenic patients

Wellcome/ Photo Researchers, Inc.

electron capture: ray-x 10

01-

11

nep

ray-x 4018

01-

4019

AreK


potassium-40 (electron capture)

Patterns of Nuclear StabilityPatterns of Nuclear Stability

Neutron-to-Proton RatioNeutron-to-Proton Ratio• The proton has high mass and high charge.• Therefore the proton-proton repulsion is large.• In the nucleus the protons are very close to each other.• The cohesive forces in the nucleus are called strong

nuclear forces. Neutrons are involved with the strong nuclear force.

• As more protons are added (the nucleus gets heavier) the proton-proton repulsion gets larger.

26

27

n/p too large

beta decay

X

n/p too small

positron decay or electron capture

Y

Neutron-to-Proton RatioNeutron-to-Proton Ratio

Neutron-to-Proton RatioNeutron-to-Proton Ratio

•The heavier the nucleus, the more neutrons are required for stability.

•The belt of stability deviates from a 1:1 neutron to proton ratio for high atomic mass.

•At Bi (83 protons) the belt of stability ends and all nuclei are unstable.

–Nuclei above the belt of stability undergo -emission. An electron is lost and the number of neutrons decreases, the number of protons increases.

Stable


20 | 29

• For stable nuclides with Z ≤ 20, the ratio of neutrons to protons is between 1 and 1.1.

• For stable nuclides with Z > 20, the ratio of neutrons to protons increases to about 1.5. This is believed to be due to the increasing repulsion between protons, which requires more neutrons to increase the strong nuclear force.

• No stable nuclide exists for Z > 83, perhaps because the proton repulsion becomes too great.

30

Nuclear Stability and Radioactive Decay

Beta decay

14C 14N + 06 7 -1

40K 40Ca + 019 20 -1

1n 1p + 00 1 -1

Decrease # of neutrons by 1

Increase # of protons by 1

Positron decay

11C 11B + 0 6 5 +1

38K 38Ar + 0 19 18 +1

1p 1n + 01 0 +1

Increase # of neutrons by 1

Decrease # of protons by 1

31

Electron capture decay

Increase number of neutrons by 1

Decrease number of protons by 1

Nuclear Stability and Radioactive Decay

37Ar + 0e 37Cl 18 17-1

55Fe + 0e 55Mn 26 25-1

1p + 0e 1n1 0-1

Alpha decay

Decrease number of neutrons by 2

Decrease number of protons by 2212Po 4He + 208Pb

84 2 82

Spontaneous fission

252Cf 2125In + 21n98 49 0

32

Nuclear binding energy is the energy required to break up a nucleus into its component protons and neutrons.

Nuclear binding energy + 19F 91p + 101n9 1 0

9 x (p mass) + 10 x (n mass) = 19.15708 amu

E = (m)c2

m= 18.9984 amu – 19.15708 amu

m = -0.1587 amu

E = -2.37 x 10-11J

E = -0.1587 amu x (3.00 x 108 m/s)2 = -1.43 x 1016 amu m2/s2

Using conversion factors:

1 kg = 6.022 x 1026 amu 1 J = kg m2/s2

33

= 2.37 x 10-11 J

19 nucleons

= 1.25 x 10-12 J/nucleon

binding energy per nucleon = binding energy

number of nucleons

E = (-2.37 x 10-11J) x (6.022 x 1023/mol)

E = -1.43 x 1013J/mol

E = -1.43 x 1010kJ/mol

Nuclear binding energy = 1.43 x 1010kJ/mol

34

Nuclear binding energy per nucleon vs mass number

nuclear stabilitynuclear binding energynucleon

Patterns of Nuclear StabilityPatterns of Nuclear StabilityNeutron-to-Proton RatioNeutron-to-Proton Ratio

– Nuclei below the belt of stability undergo +-emission or electron capture. This results in the number of neutrons increasing and the number of protons decreasing.

Nuclei with atomic numbers greater than 83 usually undergo -emission. The number of protons and neutrons decreases (in steps of 2).

Patterns of Nuclear StabilityPatterns of Nuclear StabilityRadioactive SeriesRadioactive Series For 238U, the first decay is to

234Th (-decay). The 234Th undergoes -emission to 234Pa and 234U. 234U undergoes -decay (several times) to 230Th, 226Ra, 222Rn, 218Po, and 214Pb. 214Pb undergoes -emission (twice) via 214Bi to 214Po which undergoes -decay to 210Pb. The 210Pb undergoes -emission to 210Bi and 210Po which decays () to the stable 206Pb.

37

38

Radiocarbon Dating

14N + 1n 14C + 1H7 160

14C 14N + 06 7 -1

t½ = 5730 years

Uranium-238 Dating

238U 206Pb + 8 4 + 6 092 -182 2 t½ = 4.51 x 109 years

Kelter, Mosher and Scott, Chemistry: The Practical Science, 1/e. Copyright © 2008 by Houghton Mifflin Company. Reprinted with permission.

Figure 20.19: Representation of achain reaction of nuclear fissions

Kelter, Mosher and Scott, Chemistry: The Practical Science, 1/e. Copyright © 2008 by Houghton Mifflin Company. Reprinted with permission.

Figure 20.20:An atomic bomb

Figure 20.21: Light-water nuclear reactor

Molecular views of nuclear fusion reactions of deuterons with

deuterium or tritium


20 | 44

•


20 | 45

• Nuclear Bombardment Reactions• Nuclear bombardment reactions are not

spontaneous. They involve the collision of a nucleus with another particle.

• Transmutation is the change of one element into another by bombarding the nucleus of the element with nuclear particles or nuclei.


20 | 46

• When Rutherford allowed alpha particles to collide with nitrogen nuclei, he found that a proton was ejected and oxygen was formed.


20 | 47

• Sodium-22 is made by the bombardment of magnesium-24 (the most abundant isotope of magnesium) with deuterons. An alpha particle is the other product.

He Na H Mg: Reaction 42

2211

21

2412

Na d,Mg: notation dAbbreviate 2211

2412


20 | 48

• Half-life is the time it takes for one-half of the nuclei in a sample to decay.

• Half-life is related to the decay constant by the following equation:

kt

0.693 1

2


20 | 49

•


20 | 50

• Thallium-201 is used in the diagnosis of heart disease. This isotope decays by electron capture; the decay constant is 2.63 × 10-6/s. What is the half-life of thallium-201 in days?


20 | 51

kt

0.693

21

h 24

day 1

min 60

h 1

s 60

min 1 s 10 2.63 5 t

21

s10 2.63

0.693 6-1

2

t

days 3.05 2

1 t


20 | 52

• The rate constant is related to the fraction of nuclei remaining by the following equation:

ktN

N- ln

0

t

nuclei 10 x 4.745 15tN

. time at remaining nuclei of fraction the is

. time at nuclei of number the is

nuclei. of number original the is

0

0

tN

N

tN

N

t

t


20 | 53

• A 0.500-g sample of iodine-131 is obtained by a hospital. How much will remain after a period of one week? The half-life of this isotope is 8.07 days.


20 | 54

• First, we find the value of k.

21

0.693

tk

day 7

week1 days 8.07

0.693

k

week

0.601 k


20 | 55

Next, we find the fraction of nuclei remaining.

ktN

N- ln

0

t

week1 week

0.601- ln

0

N

Nt

0.601- ln0

N

Nt

remain. nuclei of 54.8%

0.548 0

N

Nt


20 | 56

• Radioactive Dating• Because the rate of radioactive decay is constant, this

rate can serve as a sort of clock for dating objects.

• Carbon-14 is part of all living material. While a plant or animal is living, the fraction of carbon-14 in it remains constant due to exchange with the atmosphere. Once dead, the fraction of carbon-14 and, therefore, the rate of decay decrease. In this way, the fraction of carbon-14 present in the remains becomes a clock measuring the time since the plant’s or animal’s death.


20 | 57

• The half-life of carbon-14 is 5730 years. Living organisms have a carbon-14 decay rate of 15.3 disintegrations per minute per gram of total carbon.

• The ratio of disintegrations at time t to time 0 is equal to the ratio of nuclei at time t to time 0.


20 | 58

• A sample of wheat recovered from a cave was analyzed and gave 12.8 disintegrations of carbon-14 per minute per gram of carbon. What is the age of the grain?

• Carbon from living material decays at a rate of 15.3 disintegrations per minute per gram of carbon. The half-life of carbon-14 is 5730 years.


20 | 59

• Ratet = 12.8 disintegrations/min/g

• Rate0 = 15.3 disintegrations/min/g

• t1/2 = 5730 y

ln

21

0

t

NN

t

t

gtions/min/disintegra 15.3

gtions/min/disintegra 12.8

y10 1.48 3t

y57300.693

0.8366 ln

0.693

ln

0

k

NNt

0.8366 rate

rate

00

tt

N

N


20 | 60

• Energy of Nuclear Reactions

• Nuclear reactions involve changes of energy on a much larger scale than occur in chemical reactions. This energy is used in nuclear power reactors and to provide the energy for nuclear weapons.


20 | 61

• Mass–Energy Calculations

• When nuclei decay, they form products of lower energy. The change of energy is related to changes of mass, according to the equation derived by Einstein, E = mc2.


20 | 62

• Nuclear Binding Energy• The equivalence of mass and energy explains the

mass defect—that is, the difference between the total mass of the nucleons that make up an atom and the mass of the atom. The difference in mass is the energy holding the nucleus together.

• The binding energy of a nucleus is the energy needed to break a nucleus into its individual protons and neutrons.


20 | 63

•

The maximum binding energy per nucleon occurs for nuclides with mass numbers near 50

Energy Changes in Nuclear ReactionsEnergy Changes in Nuclear Reactions

23892U 234

90Th + 42He

– for 1 mol of the masses are

238.0003 g 233.9942 g + 4.015 g.– The change in mass during reaction is

233.9942 g + 4.015 g - 238.0003 g = -0.0046 g.– The process is exothermic because the system has

lost mass.

– To calculate the energy change per mole of 23892U:

J 101.4s

m-kg101.4

g 1000kg 1

g 0046.0m/s 1000.3

112

211

28

22

mcmcE

J 101.4s

m-kg101.4

g 1000kg 1

g 0046.0m/s 1000.3

112

211

28

22

mcmcE

66

Radioisotopes in Medicine

98Mo + 1n 99Mo42 0 42

235U + 1n 99Mo + other fission products92 0 42

99mTc 99Tc + -ray43 43

99Mo 99mTc + 042 43 -1

Research production of 99Mo

Commercial production of 99Mo

t½ = 66 hours

t½ = 6 hours

Bone Scan with 99mTc

67

Chemistry In Action: Food Irradiation

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