The decay constant for a radioactive nuclide is 1.5 × 10⁻⁵ s⁻¹. Atomic weight of the substance is 60 g mole⁻¹, (N_A=6×10²³). The activity of 1.0 μg of the substance is ___________ × 10¹⁰ Bq.

Solution

Physics sir · 3 steps

Activity is just lambda times N, so first turn that microgram into a count of nuclei.

1. Count the nuclei. Moles in the sample are (1.0 × 10⁻⁶ g)/(60 g mol⁻¹). Multiply by N_A to get the number of nuclei.

   N = (1.0 × 10⁻⁶)/60 × 6 × 10²³ = 1.0 × 10¹⁶

2. Apply decay law. The activity is A = λ N = 1.5 × 10⁻⁵ s⁻¹ × 1.0 × 10¹⁶ = 1.5 × 10¹¹ Bq.
3. So. In the form the question asks for, 1.5 × 10¹¹ Bq = 15 × 10¹⁰ Bq, so the answer is 15.

The common slip: 1.5. Copying the coefficient of 1.5 × 10¹¹ Bq gives 1.5. The question wants the number in front of 10¹⁰, which is 15.

The idea to keep. For activity from a mass, go mass to moles to nuclei, then multiply by λ. Keep the mass in grams when the molar mass is in grams per mole.

Answer from the NTA final answer key. Solution by PrepWiser.