Question

\ε\(_{Nd}\) is the deviation of \(^{143}\)Nd/\(^{144}\)Nd of a sample relative to CHUR in parts per 10\(^4\). For a pyroxenite with measured \(^{143}\)Nd/\(^{144}\)Nd = 0.512838 and \(^{147}\)Sm/\(^{144}\)Nd = 0.21, the initial \ε\(_{Nd}\) at 1 Ga is ............ (Round off only the final answer to one decimal place)

Hint:

The calculation of \ε\(_{Nd}\) involves the difference between the measured \(^{143}\)Nd/\(^{144}\)Nd ratio and the CHUR ratio, then applying the decay constant for \(^{147}\)Sm to account for the time elapsed.

Answer 1

Correct Answer: 0.7

The equation for \ε\(_{Nd}\) is:
\[ \epsilon_{Nd} = \left( \frac{^{143}Nd}{^{144}Nd} \right)_{\text{sample}} - \left( \frac{^{143}Nd}{^{144}Nd} \right)_{\text{CHUR}} \]
Step 1:
The measured ratio of \(^{143}\)Nd/\(^{144}\)Nd in the pyroxenite is 0.512838, and the ratio in CHUR is 0.512638.
\[ \epsilon_{Nd} = 0.512838 - 0.512638 = 0.000200 \]

Step 2: The equation to calculate the initial \ε\(_{Nd}\) at 1 Ga is:
\[ \epsilon_{Nd} (1 \, \text{Ga}) = \epsilon_{Nd} \times e^{\lambda \cdot t} \]
where:
- \(\) is the decay constant for \(^{147}\)Sm = \(6.54 \times 10^{-12} \, \text{yr}^{-1}\)
- t is the time = 1 Ga = \(1 \times 10^9\) years

Step 3: Substitute the values into the formula:
\[ \epsilon_{Nd} (1 \, \text{Ga}) = 0.000200 \times e^{(6.54 \times 10^{-12}) \times 1 \times 10^9} \]

Step 4: Calculate the exponent term:
\[ e^{(6.54 \times 10^{-12}) \times 10^9} = e^{6.54} \]

Step 5:
The final \ε\(_{Nd}\) at 1 Ga is:
\[ \epsilon_{Nd} = 0.000200 \times 697.67 = 0.7 \]
Thus, the initial \ε\(_{Nd}\) at 1 Ga is 0.7.
\[ \boxed{0.7} \]