B. Astronomers think that Earth probably formed at the same time as all of the other rocky materials in our solar system,including the oldest meteorites. The oldest meteorites ever found on Earth contain nearly equal amounts of both uranium-238 and lead-206. Based on Figure 8.10, what is Earth's age? Explain your reasoning. SOME ISOTOPES USED FOR RADIOMETRIC DATINGDaughterIsotope (D)Half-Lives (T½)Useful Dating RangeParentIsotope (P)Materials DatedNewly formedcrystalUranium-2384.5 billion years Zircon713 million years ZirconLead-206ages > 10 m.y.100Uranium-235Lead-207ages > 10 m.y.0000000oo0000015.9%decayed todaughterPotassium-40 Argon-40Biotite, muscovite,whole volcanic rock1.3 billion yearsages > 50,000 yrShells, limestone,organic materialsages 100-60,000 yrCarbon-14Nitrogen-145730 years84.129.3%decayed70.7ParentAtoms (P)000000000e50%decayedRADIOACTIVEDECAY50.0DaughterAtoms (D)25.075% decayed87.5%decayed12.593.8%decayed96.9%decayed6.23.11423456Half-Lives (T1) ElapsedDECAY PARAMETERS FOR ALL RADIOACTIVE DECAY PAIRSPercent ofParentAtoms (P)Percent ofDaughterAtoms (D)Half-LivesElapsedAge0.000 x T0.015 x T0.031 x Ty0.062 x Ty0.125 x T0.250 x T0.500 x T21.000 x Ty2100.00.098.91.11/6497.92.11/3295.84.21/1691.78.31/884.115.91/470.729.31/250.050.011'½1.500 x T,2.000 x T3.000 x T4.000 x Ty5.000 x Ty235.464.625.075.0212.587.536.293.843.196.9Percent of Parent (P) Atoms Remaining

The Uranium-238 radioactively disintegrates into Lead-206. The half life of this nuclear reaction is…

SOME ISOTOPES USED FOR RADIOMETRIC DATING Daughter Isotope (D) Useful Dating Range Newly formed crystal Parent Isotope (P) Half-Lives (T,) Materials Dated 100 Uranium-238 Lead-206 4.5 billion years Zircon ages > 10 m.y. Uranium-235 Lead-207 713 million years Zircon |15.9% daughter 1.3 billion years Biotite, muscovite, whole volcanic rock ages > 10 m.y. ages > 50,000 yr Potassium-40 Argon-40 000 ecayed to Shells, limestone, organic materials Carbon-14 Nitrogen-14 5730 years ages 100-60,000 yr 84.1 29.3% decayed 70.7 Parent Atoms (P) RADIOACTIVE DECAY 50.0 50% decayed Daughter Atoms (D) 25.0 75% decayed 87.5% decayed 12.5 93.8% decayed 96.9% decayed 6.2 3.1 2 3 Half-Lives (T,) Elapsed DECAY PARAMETERS FOR ALL RADIOACTIVE DECAY PAIRS Percent of Parent Atoms (P) Percent of Daughter Atoms (D) Half-Lives Elapsed Age 0.000 x T 0.015 x T 0.031 x Ty 0.062 x T 0.125 x T 0.250 x Ty 100.0 0.0 98.9 1.1 1/64 97.9 2.1 1/32 95.8 4.2 1/16 91.7 8.3 1/8 84.1 15.9 1/4 70.7 29.3 1/2 0.500 x Ty. 1.000 x T 1.500 x T 2.000 x T, 3.000 x T, 4.000 x T 5.000 x T 50.0 50.0 35.4 64.6 1'½ 25.0 75.0 2 12.5 87.5 3 6.2 93.8 4 3.1 96.9 Percent of Parent (P) Atoms Remaining

SOME ISOTOPES USED FOR RADIOMETRIC DATING Daughter Isotope (D) Useful Dating Range Newly formed crystal Parent Isotope (P) Half-Lives (T,) Materials Dated 100 Uranium-238 Lead-206 4.5 billion years Zircon ages > 10 m.y. Uranium-235 Lead-207 713 million years Zircon |15.9% daughter 1.3 billion years Biotite, muscovite, whole volcanic rock ages > 10 m.y. ages > 50,000 yr Potassium-40 Argon-40 000 ecayed to Shells, limestone, organic materials Carbon-14 Nitrogen-14 5730 years ages 100-60,000 yr 84.1 29.3% decayed 70.7 Parent Atoms (P) RADIOACTIVE DECAY 50.0 50% decayed Daughter Atoms (D) 25.0 75% decayed 87.5% decayed 12.5 93.8% decayed 96.9% decayed 6.2 3.1 2 3 Half-Lives (T,) Elapsed DECAY PARAMETERS FOR ALL RADIOACTIVE DECAY PAIRS Percent of Parent Atoms (P) Percent of Daughter Atoms (D) Half-Lives Elapsed Age 0.000 x T 0.015 x T 0.031 x Ty 0.062 x T 0.125 x T 0.250 x Ty 100.0 0.0 98.9 1.1 1/64 97.9 2.1 1/32 95.8 4.2 1/16 91.7 8.3 1/8 84.1 15.9 1/4 70.7 29.3 1/2 0.500 x Ty. 1.000 x T 1.500 x T 2.000 x T, 3.000 x T, 4.000 x T 5.000 x T 50.0 50.0 35.4 64.6 1'½ 25.0 75.0 2 12.5 87.5 3 6.2 93.8 4 3.1 96.9 Percent of Parent (P) Atoms Remaining

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Radioactive decay

The emission of energy to produce ionizing radiation is known as radioactive decay. Alpha, beta particles, and gamma rays are examples of ionizing radiation that could be released. Radioactive decay happens in radionuclides, which are imbalanced atoms. This periodic table's elements come in a variety of shapes and sizes. Several of these kinds are stable like nitrogen-14, hydrogen-2, and potassium-40, whereas others are not like uranium-238. In nature, one of the most stable phases of an element is usually the most prevalent. Every element, meanwhile, has an unstable state. Unstable variants are radioactive and release ionizing radiation. Certain elements, including uranium, have no stable forms and are constantly radioactive. Radionuclides are elements that release ionizing radiation.

Artificial Radioactivity

The radioactivity can be simply referred to as particle emission from nuclei due to the nuclear instability. There are different types of radiation such as alpha, beta and gamma radiation. Along with these there are different types of decay as well.

Question

B. Astronomers think that Earth probably formed at the same time as all of the other rocky materials in our solar system,
including the oldest meteorites. The oldest meteorites ever found on Earth contain nearly equal amounts of both uranium-
238 and lead-206. Based on Figure 8.10, what is Earth's age? Explain your reasoning.

SOME ISOTOPES USED FOR RADIOMETRIC DATING
Daughter
Isotope (D)
Half-Lives (T½)
Useful Dating Range
Parent
Isotope (P)
Materials Dated
Newly formed
crystal
Uranium-238
4.5 billion years Zircon
713 million years Zircon
Lead-206
ages > 10 m.y.
100
Uranium-235
Lead-207
ages > 10 m.y.
0000000o
o00000
15.9%
decayed to
daughter
Potassium-40 Argon-40
Biotite, muscovite,
whole volcanic rock
1.3 billion years
ages > 50,000 yr
Shells, limestone,
organic materials
ages 100-60,000 yr
Carbon-14
Nitrogen-14
5730 years
84.1
29.3%
decayed
70.7
Parent
Atoms (P)
000000000e
50%
decayed
RADIOACTIVE
DECAY
50.0
Daughter
Atoms (D)
25.0
75% decayed
87.5%
decayed
12.5
93.8%
decayed
96.9%
decayed
6.2
3.1
14
2
3
4
5
6
Half-Lives (T1) Elapsed
DECAY PARAMETERS FOR ALL RADIOACTIVE DECAY PAIRS
Percent of
Parent
Atoms (P)
Percent of
Daughter
Atoms (D)
Half-Lives
Elapsed
Age
0.000 x T
0.015 x T
0.031 x Ty
0.062 x Ty
0.125 x T
0.250 x T
0.500 x T2
1.000 x Ty2
100.0
0.0
98.9
1.1
1/64
97.9
2.1
1/32
95.8
4.2
1/16
91.7
8.3
1/8
84.1
15.9
1/4
70.7
29.3
1/2
50.0
50.0
1
1'½
1.500 x T,
2.000 x T
3.000 x T
4.000 x Ty
5.000 x Ty2
35.4
64.6
25.0
75.0
2
12.5
87.5
3
6.2
93.8
4
3.1
96.9
Percent of Parent (P) Atoms Remaining

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