A lunar soil sample was analysed for its isotopic xenon content. The amount of Xe¹²⁹ was 4.48 mm³ (STP) per kg of soil. Radiochemical analysis showed that only one-fourth of these Xe¹²⁹ atoms were pro

Question

A lunar soil sample was analysed for its isotopic xenon content. The amount of Xe¹²⁹ was 4.48 mm³ (STP) per kg of soil. Radiochemical analysis showed that only one-fourth of these Xe¹²⁹ atoms were produced by cosmic events (the rest are primordial). If each cosmic event produces exactly one Xe¹²⁹ atom and the number of events per kg of soil is X, then the value of X/10¹⁶ is (R = 8.4 J/K-mol, N A = 6.0 × 10²³)

TestHub · Accepted Answer

Volume at STP = 4.48 mm³ = 4.48 × 10⁻⁶ L; moles of Xe = 4.48 × 10⁻⁶/22.4 = 2.0 × 10⁻⁷ mol.

Total atoms = 2.0 × 10⁻⁷ x 6.0 × 10²³ = 1.2 × 10¹⁷.

Event-produced atoms (events) X = (1/4) × 1.2 × 10¹⁷ = 3.0 × 10¹⁶.

X/10¹⁶ = 3. (R is given but not needed; STP molar volume 22.4 L suffices.)

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