Isotope Geochemistry Questions and Answers

Q: Which one of the following Uranium isotopes is not occurring in the nature ?

The isotope that does not occur naturally is \(\mathrm{U}^{232}\).Natural uranium consists of 238U (about 99.27%), 235U (about 0.72%) and a trace of 234U, which is continually produced in the decay chain of 238U.232U, with a half-life of about 69 years, is produced artificially in nuclear reactors, notably as a by-product in the thorium fuel cycle. Its short half-life means none could have survived from the formation of the Earth, and no natural decay chain produces it in measurable amounts.

Q: How much time will be required for a sample of hydrogen-3 to lose 75% of its radioactivity ? Half life of tritium is 12.26 years :

The time required is about 24.5 years.Losing 75% of the activity means 25% remains, which is one quarter, or two half-lives:\[ \begin{aligned} \frac{N}{N_{0}} &= \left(\frac{1}{2}\right)^{n} = \frac{1}{4} \Rightarrow n = 2 \\ t &= 2 \times 12.26 = 24.52\ \text{years} \end{aligned} \]36.8 years is three half-lives (87.5% lost), 49 years is four half-lives (93.75% lost), and 20.6 years corresponds to no whole number of half-lives for this loss.

Q: Which one of the following decay series is incorrect along with their half life ?

The incorrect pair is Uranium-235 to Lead-350 at 200 million years.Uranium-235 decays through a chain of alpha and beta decays to lead-207, not lead-350 (no lead isotope has a mass number anywhere near 350), and its half-life is about 704 million years, not 200 million.The other three are correct. Carbon-14 decays to nitrogen-14 with a half-life of 5,730 years, the basis of radiocarbon dating. Potassium-40 decays partly to argon-40 with a half-life of about 1,250-1,280 million years, used in K-Ar dating. Rubidium-87 decays to strontium-87 with a half-life of about 48,800 million years, used in Rb-Sr dating.

Q: The depleted MORB Mantle (DMM) reservoir shows following Sr-Nd isotopic compositions :

DMM has low 87Sr/86Sr and high 143Nd/144Nd.The depleted MORB mantle has lost incompatible elements to the continental crust over Earth history. Rb is more incompatible than Sr, so the residue has a low Rb/Sr ratio and has produced little radiogenic 87Sr. Nd is more incompatible than Sm, so the residue has a high Sm/Nd ratio and has grown more radiogenic 143Nd, giving positive \(\varepsilon_{\text{Nd}}\).High Sr with low Nd ratios describes enriched sources, such as continental crust and EM2-type mantle. The other two combinations do not match the coupled Rb-Sr and Sm-Nd behaviour of a depleted reservoir.

Q: The following isotopic ratio is useful in constraining the time of separation of melt from the enriched or depleted mantle :

The useful ratio is 143Nd/144Nd.Sm-147 decays to Nd-143, and a rock's measured 143Nd/144Nd together with its Sm/Nd ratio can be traced back to the time when its isotopic composition matched a model mantle reservoir. This gives a Nd model age (TCHUR or TDM), the time the melt separated from chondritic or depleted mantle.The other ratios are printed with impossible mass numbers or are not used this way: strontium has no isotope of mass 57 (Sr ratios use 87 and 86), and there is no lead-297. 206Pb/238U is a U-Pb geochronometer that dates crystallisation of minerals such as zircon, not separation from a mantle source.

Q: In nuclear energy production, the processed or enriched Uranium is :

Enriched uranium is enriched in U-235.Natural uranium is about 99.3% U-238 and only about 0.7% U-235. U-235 is the fissile isotope that sustains a chain reaction with slow neutrons, so for most reactors uranium is processed to raise the U-235 content to about 3-5%; weapons need about 90%.U-238 is the abundant isotope that is reduced in proportion by enrichment, ending up in depleted uranium. U-234 is a minor decay product present in tiny amounts. U-232 is an artificial isotope, a troublesome contaminant in the thorium fuel cycle, not the enriched fuel.

11.

Which one of the following Uranium isotopes is not occurring in the nature ?

A.\(\mathrm{U}^{235}\)
B.\(\mathrm{U}^{234}\)
C.\(\mathrm{U}^{238}\)
D.\(\mathrm{U}^{232}\)

Exam Year(s)

MH SET - 2024, SET Exam - 2024,

Answer: D

The isotope that does not occur naturally is \(\mathrm{U}^{232}\).

Natural uranium consists of ²³⁸U (about 99.27%), ²³⁵U (about 0.72%) and a trace of ²³⁴U, which is continually produced in the decay chain of ²³⁸U.

²³²U, with a half-life of about 69 years, is produced artificially in nuclear reactors, notably as a by-product in the thorium fuel cycle. Its short half-life means none could have survived from the formation of the Earth, and no natural decay chain produces it in measurable amounts.

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12.

How much time will be required for a sample of hydrogen-3 to lose 75% of its radioactivity ? Half life of tritium is 12.26 years :

A.36.8 years
B.24.5 years
C.49 years
D.20.6 years

Exam Year(s)

MH SET - 2024, SET Exam - 2024,

Answer: B

The time required is about 24.5 years.

Losing 75% of the activity means 25% remains, which is one quarter, or two half-lives:

\[ \begin{aligned} \frac{N}{N_{0}} &= \left(\frac{1}{2}\right)^{n} = \frac{1}{4} \Rightarrow n = 2 \\ t &= 2 \times 12.26 = 24.52\ \text{years} \end{aligned} \]

36.8 years is three half-lives (87.5% lost), 49 years is four half-lives (93.75% lost), and 20.6 years corresponds to no whole number of half-lives for this loss.

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13.

Which one of the following decay series is incorrect along with their half life ?

A.Carbon-14 to Nitrogen-14 at 5730 years
B.Uranium-235 to Lead-350 at 200 million years
C.Potassium-40 to Argon-40 at 1280 million years
D.Rubidium-87 to Strontium-87 at 48,800 million years

Exam Year(s)

MH SET - 2025, SET Exam - 2025,

Answer: B

The incorrect pair is Uranium-235 to Lead-350 at 200 million years.

Uranium-235 decays through a chain of alpha and beta decays to lead-207, not lead-350 (no lead isotope has a mass number anywhere near 350), and its half-life is about 704 million years, not 200 million.

The other three are correct. Carbon-14 decays to nitrogen-14 with a half-life of 5,730 years, the basis of radiocarbon dating. Potassium-40 decays partly to argon-40 with a half-life of about 1,250-1,280 million years, used in K-Ar dating. Rubidium-87 decays to strontium-87 with a half-life of about 48,800 million years, used in Rb-Sr dating.

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14.

The depleted MORB Mantle (DMM) reservoir shows following Sr-Nd isotopic compositions :

A.High \(^{87}\)Sr/\(^{86}\)Sr and low \(^{143}\)Nd/\(^{144}\)Nd
B.Low \(^{87}\)Sr/\(^{86}\)Sr and low \(^{143}\)Nd/\(^{144}\)Nd
C.Low \(^{87}\)Sr/\(^{86}\)Sr and high \(^{143}\)Nd/\(^{144}\)Nd
D.High \(^{87}\)Sr/\(^{86}\)Sr and high \(^{143}\)Nd/\(^{144}\)Nd

Exam Year(s)

MH SET - 2025, SET Exam - 2025,

Answer: C

DMM has low ⁸⁷Sr/⁸⁶Sr and high ¹⁴³Nd/¹⁴⁴Nd.

The depleted MORB mantle has lost incompatible elements to the continental crust over Earth history. Rb is more incompatible than Sr, so the residue has a low Rb/Sr ratio and has produced little radiogenic ⁸⁷Sr. Nd is more incompatible than Sm, so the residue has a high Sm/Nd ratio and has grown more radiogenic ¹⁴³Nd, giving positive \(\varepsilon_{\text{Nd}}\).

High Sr with low Nd ratios describes enriched sources, such as continental crust and EM2-type mantle. The other two combinations do not match the coupled Rb-Sr and Sm-Nd behaviour of a depleted reservoir.

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15.

The following isotopic ratio is useful in constraining the time of separation of melt from the enriched or depleted mantle :

A.\(^{86}\)Sr/\(^{57}\)Sr
B.\(^{143}\)Nd/\(^{144}\)Nd
C.\(^{206}\)Pb/\(^{238}\)U
D.\(^{297}\)Pb/\(^{235}\)U

Exam Year(s)

MH SET - 2025, SET Exam - 2025,

Answer: B

The useful ratio is ¹⁴³Nd/¹⁴⁴Nd.

Sm-147 decays to Nd-143, and a rock's measured ¹⁴³Nd/¹⁴⁴Nd together with its Sm/Nd ratio can be traced back to the time when its isotopic composition matched a model mantle reservoir. This gives a Nd model age (T_CHUR or T_DM), the time the melt separated from chondritic or depleted mantle.

The other ratios are printed with impossible mass numbers or are not used this way: strontium has no isotope of mass 57 (Sr ratios use 87 and 86), and there is no lead-297. ²⁰⁶Pb/²³⁸U is a U-Pb geochronometer that dates crystallisation of minerals such as zircon, not separation from a mantle source.

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16.

In nuclear energy production, the processed or enriched Uranium is :

A.U\(^{238}\)
B.U\(^{234}\)
C.U\(^{232}\)
D.U\(^{235}\)

Exam Year(s)

MH SET - 2025, SET Exam - 2025,

Answer: D

Enriched uranium is enriched in U-235.

Natural uranium is about 99.3% U-238 and only about 0.7% U-235. U-235 is the fissile isotope that sustains a chain reaction with slow neutrons, so for most reactors uranium is processed to raise the U-235 content to about 3-5%; weapons need about 90%.

U-238 is the abundant isotope that is reduced in proportion by enrichment, ending up in depleted uranium. U-234 is a minor decay product present in tiny amounts. U-232 is an artificial isotope, a troublesome contaminant in the thorium fuel cycle, not the enriched fuel.

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