Part (a) is done. Please do parts (b) and (c).

SM-ND EVOLUTION (a) (1 point) 147Sm decays to 143Nd through alpha decay with a decay constant of 147=6.54E-12. Write the equation describing how 143Nd changes over time (use 147, 147Sm, and 143Ndinitial and normalize to 144Nd). 1900 Liquid Olivine Liquid Olivine 208080 Fo W.% Forstarite 1143N 144 Nd/ T - HIN +/ 44 Nalo Figure 1: Olivine phase diagram. Fa is Fayalite (F2S106) and Fois Forsterite Mg2S104) Label this diagram with letters as you wer the question (b) (1 point) Rearrange your equation from (a) to solve for initial 143Nd/144 Nd. With this equation you can calculate how the daughter isotope has evolved over time. Typically, we assume that the primitive mantle of Earth has the same isotopic composition of chondrites. We call this the Chondritic uniform reservoir (CHUR). Some portion of the modern man- tle has been depleted in incompatible trace elements such as Sm and Nd. The following table contains the approximate isotopic composition of this depleted mantle reservoir and CHUR: Sample CHUR Depleted Mantle 143Nd/144Nd 0.512538 0.513051 147Sm/144Nd 0.1967 0.2137 Make a single figure (your Figure 1) with a line illustrating how 143Nd/144Nd in CHUR and the depleted mantle evolve over the history of Earth (4.543 Ga to today). Make sure it is clear which line represents which reservoir through a legend or annotation. Your X-axis should be the age, and the y-axis should be the isotopic ratio. Have CHUR and the depleted mantle had the same Nd isotopic composition in the past? Approximately when? (c) (2 points) Variations in 143Nd/144Nd between reservoirs are usually quite small. A con- vention for describing these small variations is to define a new scale relative to the CHUR model, known as the epsilon Nd (END). 143 Nd 144Nd) CHUR x 10000 144Nd d/SAMPLE END = - 143 Nd (144 NdCHUR (2) Update your Figure 1 to this eNd scale (change the y-axis). This new figure will be your Figure 2 and you will add components to it over the next few questions. What is the end if the depleted mantle? SM-ND EVOLUTION (a) (1 point) 147Sm decays to 143Nd through alpha decay with a decay constant of 147=6.54E-12. Write the equation describing how 143Nd changes over time (use 147, 147Sm, and 143Ndinitial and normalize to 144Nd). 1900 Liquid Olivine Liquid Olivine 208080 Fo W.% Forstarite 1143N 144 Nd/ T - HIN +/ 44 Nalo Figure 1: Olivine phase diagram. Fa is Fayalite (F2S106) and Fois Forsterite Mg2S104) Label this diagram with letters as you wer the question (b) (1 point) Rearrange your equation from (a) to solve for initial 143Nd/144 Nd. With this equation you can calculate how the daughter isotope has evolved over time. Typically, we assume that the primitive mantle of Earth has the same isotopic composition of chondrites. We call this the Chondritic uniform reservoir (CHUR). Some portion of the modern man- tle has been depleted in incompatible trace elements such as Sm and Nd. The following table contains the approximate isotopic composition of this depleted mantle reservoir and CHUR: Sample CHUR Depleted Mantle 143Nd/144Nd 0.512538 0.513051 147Sm/144Nd 0.1967 0.2137 Make a single figure (your Figure 1) with a line illustrating how 143Nd/144Nd in CHUR and the depleted mantle evolve over the history of Earth (4.543 Ga to today). Make sure it is clear which line represents which reservoir through a legend or annotation. Your X-axis should be the age, and the y-axis should be the isotopic ratio. Have CHUR and the depleted mantle had the same Nd isotopic composition in the past? Approximately when? (c) (2 points) Variations in 143Nd/144Nd between reservoirs are usually quite small. A con- vention for describing these small variations is to define a new scale relative to the CHUR model, known as the epsilon Nd (END). 143 Nd 144Nd) CHUR x 10000 144Nd d/SAMPLE END = - 143 Nd (144 NdCHUR (2) Update your Figure 1 to this eNd scale (change the y-axis). This new figure will be your Figure 2 and you will add components to it over the next few questions. What is the end if the depleted mantle