A radioactive nuclide has decay constant 1.5 × 10⁻⁵ s⁻¹ and molar mass 60 g mol⁻¹. Take N(A) = 6 × 10²³ mol⁻¹. The activity of 1.0 μg of the substance is ______ × 10¹⁰ Bq.
Physics · Circular Motion
JEE Mains 10 April 2023 Shift 1 Morning Shift

Question

A radioactive nuclide has decay constant 1.5 × 10⁻⁵ s⁻¹ and molar mass 60 g mol⁻¹. Take N(A) = 6 × 10²³ mol⁻¹. The activity of 1.0 μg of the substance is ______ × 10¹⁰ Bq.

G1 Physics · Accepted Answer

Mass = 1.0 μg = 1×10⁻⁶ g Number of moles: n = (1×10⁻⁶)/60 Number of atoms: N = nN(A) = [(1×10⁻⁶)/60](6×10²³) = 1×10¹⁶ Activity: A = λN = (1.5×10⁻⁵)(1×10¹⁶) = 1.5×10¹¹ Bq = 15×10¹⁰ Bq Final value: 15