As indicated in the chapter, geothermal heat comes primarily from the radioactive decay of uranium, thorium, and potassium. The isotopes of these elements that contribute to the radioactivity and their half-lives are: ${ } ^ { 235 } \mathrm { U } \left( 7.1 \times 10 ^ { 8 } \right.$ years $) , { } ^ { 238 } \mathrm { U } ( 4.5 \times$ $10 ^ { 9 }$ years $) , { } ^ { 232 } \mathrm { Th } \left( 1.4 \times 10 ^ { 10 } \right.$ years $)$, and ${ } ^ { 40 } \mathrm {~K} \left( 1.4 \times 10 ^ { 9 } \right.$ years $)$. Assume that these four nuclides existed in equal quantities at the time the earth was formed $4.54 \times 10 ^ { 9 }$ years ago.
(a) What are the relative proportions of each nuclide at present?
(b) What are the relative contributions of each nuclide to the total radioactive decay in the earth?

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The Answer of As indicated in the chapter, geothermal heat comes primarily from the radioactive decay of uranium, thorium, and potassium. The isotopes of these elements that contribute to the radioactivity and their half-lives are: ${ } ^ { 235 } \mathrm { U } \left( 7.1 \times 10 ^ { 8 } \right.$ years $) , { } ^ { 238 } \mathrm { U } ( 4.5 \times$ $10 ^ { 9 }$ years $) , { } ^ { 232 } \mathrm { Th } \left( 1.4 \times 10 ^ { 10 } \right.$ years $)$, and ${ } ^ { 40 } \mathrm {~K} \left( 1.4 \times 10 ^ { 9 } \right.$ years $)$. Assume that these four nuclides existed in equal quantities at the time the earth was formed $4.54 \times 10 ^ { 9 }$ years ago.
(a) What are the relative proportions of each nuclide at present?
(b) What are the relative contributions of each nuclide to the total radioactive decay in the earth?

As Indicated in the Chapter, Geothermal Heat Comes Primarily from the Radioactive