Uranium dating technique can be used to predict the age of the earth. The principle behind this technique is that \( { }^{236} \mathrm{U} \) undergoes radioactive decay to form stable \( { }^{206} \mathrm{~Pb} \). The age of the earth can be determined by measuring the ratio of \( { }^{206} \mathrm{~Pb} \) to \( { }^{238} \mathrm{U} \).
\( \frac{\text { Number of atoms of } \mathrm{Pb}^{206} \text { formed }}{\text { Number of atoms of } \mathrm{U}^{23} \text { left }}=e^{-\lambda t-1} \)
Similarly, \( { }^{235} \mathrm{U} \) decays to \( { }^{207} \mathrm{~Pb} \), and \( { }^{232} \) Th decays to \( { }^{208} \mathrm{~Pb} \). The radioactive isotope of carbon, \( { }^{14} \mathrm{C} \), produced by the bombardment of nitrogen atoms by neutrons is also used for determining the age of earth by knowing the ratio of \( { }^{14} \mathrm{C} /{ }^{12} \mathrm{C} \).
Which of the following ratio cannot be used for determining the age of a rock?
(A) \( { }^{206} \mathrm{~Pb} /{ }^{238} \mathrm{U} \)
(B) \( { }^{206} \mathrm{~Pb} /{ }^{235} \mathrm{U} \)
(C) \( { }^{208} \mathrm{~Pb} /{ }^{232} \mathrm{U} \)
(D) \( { }^{207} \mathrm{~Pb} /{ }^{235} \mathrm{U} \)
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