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Nuclear Reactions and Their Applications

23.1Radioactive Decay and Nuclear Stability

23.2The Kinetics of Radioactive Decay

23.3Nuclear Transmutation: Induced Changes in Nuclei

23.4The Effects of Nuclear Radiation on Matter

23.5Applications of Radioisotopes

23.6The Interconversion of Mass and Energy

23.7Applications of Fission and Fusion

The behavior of three types of radioactive emissions in an electric field.

Figure 23.1

Types of Radioactive Decay: Balancing Nuclear Equations

Total ATotal Z Reactants = Total ATotal Z Products

Alpha decay - A decreases by 4 and Z decreases by 2. Every element heavier than Pb undergoes a decay.

Beta decay - ejection of a b particle from the nucleus from the conversion of a neutron into a proton and the expulsion of 0-1b. The product nuclide will have the same Z but will be one atomic number higher.

Positron decay - a positron (01b) is the antiparticle of an electron. A proton in the nucleus is converted into a neutron with the expulsion of the positron. Z remains the same but the atomic number decreases.

Electron capture - a nuclear proton is converted into a neutron by the capture of an electron. Z remains the same but the atomic number decreases.

Gamma emission - energy release; no change in Z or A.

Write balanced equations for the following nuclear reactions:

(a) 23290Th 22888Ra + 42He

23290Th 22888Ra + 42He

(b) 3617Cl + 0-1e AZX

3617Cl + 0-1e 3616S

Sample Problem 23.1

Writing Equations for Nuclear Reactions

(a) Naturally occurring thorium-232 undergoes a decay.

(b) Chlorine-36 undergoes electron capture.

PLAN:

Write a skeleton equation; balance the number of neutrons and charges; solve for the unknown nuclide.

SOLUTION:

A = 228 and Z = 88

A = 36 and Z = 16

Nuclear Stability and Mode of Decay

- Very few stable nuclides exist with N/Z < 1.

- The N/Z ratio of stable nuclides gradually increases a Z increases.

- All nuclides with Z > 83 are unstable.

- Elements with an even Z usually have a larger number of stable nuclides than elements with an odd Z.

- Well over half the stable nuclides have both even N and even Z.

Predicting the Mode of Decay

- Neutron-rich nuclides undergo b decay.

- Neutron-poor nuclides undergo positron decay or electron capture.

- Heavy nuclides undergo a decay.

Which of the following nuclides would you predcit to be stable and which radioactive? Explain.

Sample Problem 23.2

Predicting Nuclear Stability

(a)1810Ne

(b)3216S

(c)23690Th

(d)12356Ba

PLAN:

Stability will depend upon the N/Z ratio, the value of Z, the value of stable N/Z nuclei, and whether N and Z are even or odd.

SOLUTION:

(a) Radioactive.

(b) Stable.

N/Z = 0.8; there are too few neutrons to be stable.

N/Z = 1.0; Z < 20 and N and Z are even.

(d) Radioactive.

(c) Radioactive.

N/Z = 1.20; the diagram on shows stability when N/Z ≥ 1.3.

Every nuclide with Z > 83 is radioactive.

Predict the nature of the nuclear change(s) each of the following radioactive nuclides is likely to undergo:

(a) N/Z = 1.4 which is high.

The nuclide will probably undergo b decay altering Z to 6 and lowering the ratio.

Sample Problem 23.3

Predicting the Mode of Nuclear Decay

(a)125B

(b)23492U

(c)7433As

(d)12757La

PLAN:

Find the N/Z ratio and compare it to the band stability. Then predict which of the modes of decay will give a ratio closer to the band.

SOLUTION:

(b) The large number of neutrons makes this a good candidate for a decay.

(c) N/Z = 1.24 which is in the band of stability. It will probably undergo b decay or positron emission.

(d) N/Z = 1.23 which is too low for this area of the band. It can increase Z by positron emission or electron capture.

Figure 23.3

SI unit of decay is the becquerel (Bq) = 1d/s.

curie (Ci) =

number of nuclei disintegrating each second in 1g of radium-226 =

3.70x1010d/s

Nuclear decay is a first-order rate process.

Large k means a short half-life and vice versa.

Strontium-90 is a radioactive by-product of nuclear reactors that behaves biologically like calcium, the element above it in Group 2A(2). When 90Sr is ingested by mammals, it is found in their milk and eventually in the bones of those drinking the milk. If a sample of 90Sr has an activity of 1.2x1012 d/s, what are the activity and the fraction of nuclei that have decayed after 59 yr (t1/2 of 90Sr = 29 yr)

(1.2x1012-2.9x1011)

Fraction decayed

Fraction decayed

=

=

(1.2x1012)

0.76

Sample Problem 23.4

Finding the Number of Radioactive Nuclei

PLAN:

The fraction of nuclei that have decayed is the change in the number of nuclei, expressed as a fraction of the starting number. The activity of the sample (A) is proportional to the number of nuclei (N). We are given the A0 and can find A from the integrated form of the first-order rate equation.

SOLUTION:

t1/2 = ln2/k so k = 0.693/29 yr

= 0.024 yr-1

ln N0/Nt = ln A0/At = kt

ln At = -kt + ln A0

ln At = -(0.024yr-1)(59yr) + ln(1.2x1012d/s)

ln At = 26.4

At = 2.9x1011d/s

The charred bones of a sloth in a cave in Chile represent the earliest evidence of human presence in the southern tip of South America. A sample of the bone has a specific activity of 5.22 disintegrations per minute per gram of carbon (d/min*g). If the ratio of 12C:14C in living organisms results in a specific activity of 15.3 d/min*g, how old are the bones? (t1/2 of 14C = 5730 yr)

PLAN:

Calculate the rate constant using the given half-life. Then use the first-order rate equation to find the age of the bones.

Sample Problem 23.5

Applying Radiocarbon Dating

SOLUTION:

k = ln 2/t1/2 = 0.693/5730yr

= 1.21x10-4yr-1

t = 1/k ln A0/At =

1/(1.21x10-4yr-1) ln (15.3/5.22)

= 8.89x103 yr

The bones are about 8900 years old.

Figure 23.6

Penetrating power of radioactive emissions.

Nuclear changes cause chemical changes in surrounding matter by excitation and ionization.

Penetrating power is inversely related to the mass and charge of the emission.

The use of radioisotopes to image the thyroid gland.

asymmetric scan indicates disease

normal

Figure 23.10

PET and brain activity.

normal

Alzheimer’s

The increased shelf life of irradiated food.

Figure 23.11

The Interconversion of Mass and Energy

The mass of the nucleus is less than the combined masses of its nucleons. The mass decrease that occurs when nucleons are united into a nucleus is called the mass defect.

E = mc2

DE = Dmc2

Dm = DE / c2

The mass defect (Dm) can be used to calculate the nuclear binding energyin MeV.

1 amu = 931.5x106 eV = 931.5 MeV

Iron-56 is an extremely stable nuclide. Compute the binding energy per nucleon for 56Fe and compare it with that for 12C (mass of 56Fe atom = 55.934939 amu; mass of 1H atom = 1.007825 amu; mass of neutron = 1.008665 amu).

(0.52846 amu)(931.5 MeV/amu)

56 nucleons

Sample Problem 23.6

Calculating the Binding Energy per Nucleon

PLAN:

Find the mass defect, Dm; multiply that by the MeV equivalent and divide by the number of nucleons.

SOLUTION:

Mass Defect = [(26 x 1.007825 amu) + (30 x 1.008665 amu)] - 55.934939

Dm = 0.52846 amu

Binding energy =

= 8.790 Mev/nucleon

12C has a binding energy of 7.680 MeV/nucleon, so 56Fe is more stable.

The variation in binding energy per nucleon.

Figure 23.12

Figure 23.13

Figure 23.14

Schematic of a light-water nuclear reactor.

The tokamak design for magnetic containment of a fusion plasma.

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